Level 2 Geometry Spring 2012 Ms. Katz.

Level 2 Geometry Spring 2012 Ms. Katz

Day 1: January 30th Objective: Form and meet study teams. Then work together to build symmetrical designs using the same basic shapes. Seats and Fill out Index Card (questions on next slide) Introduction: Ms. Katz, Books, Syllabus, Homework Record, Expectations Problems 1-1 and 1-2 Möbius Strip Demonstration Conclusion Homework: Have parent/guardian fill out last page of syllabus and sign; Problems 1-3 to 1-7 AND 1-17 to 1-18; Extra credit tissues or hand sanitizer (1)

Respond on Index Card: When did you take Algebra 1?
Who was your Algebra 1 teacher? What grade do you think you earned in Algebra 1? What is one concept/topic from Algebra 1 that Ms. Katz could help you learn better? What grade would you like to earn in Geometry? (Be realistic) What sports/clubs are you involved in this Spring? My address (for teacher purposes only) is:

Support www.cpm.org www.hotmath.com My Webpage on the HHS website
Resources (including worksheets from class) Extra support/practice Parent Guide Homework Help All the problems from the book Homework help and answers My Webpage on the HHS website Classwork and Homework Assignments Worksheets Extra Resources

Quilts

1-1: First Resource Page

1-1: Second Resource Page
Write sentence and names around the gap. Cut along dotted line Glue sticks are rewarded when 4 unique symmetrical designs are shown to the teacher.

Day 2: January 31st Objective: Use your spatial visualization skills to investigate reflection. THEN Understand the three rigid transformations (translations, reflections, and rotations) and learn some connections between them. Also, introduce notation for corresponding parts. Homework Check and Correct (in red) – Collect last page of syllabus “Try This!” Algebra Review (x2) LL – “Graphing an Equation” Problems 1-48 to 1-51, 1-53 Problems 1-59 to 1-61 LL – “Rigid Transformations” Conclusion Homework: Problems 1-54 to 1-58 AND 1-63 to 1-67; GET SUPPLIES; Extra credit tissues or hand sanitizer (1)

Try This! Algebra Review
Complete the table below for y = -2x+5 Write a rule relating x and y for the table below. x -3 -1 2 4 7 y 11 5 1 -9 x -3 -1 2 4 7 y y = 3x+4 x 1 2 3 4 5 6 y 7 10 13 16 19 22 13 13

A Complete Graph y = -2x+5 Create a table of x-values
Use the equation to find y-values Complete the graph by scaling and labeling the axes Graph and connect the points from your table. Then label the line. 10 y = -2x+5 5 x -4 -3 -2 -1 1 2 3 4 y 13 11 9 7 5 x -10 -5 5 10 -5 -10

Try This! Algebra Review
Solve the following Equation for x and check your answer: 6x + 3 – 10 = x x 15 15

Solving Linear Equations (pg 19)
Simplify each side: Combine like terms Keep the equation balanced: Anything added or taken away from one side, must also be added or taken away from the other Move the x-terms to one side of the equations: Isolate the letters on one side Undo operations: Remember that addition and subtraction are opposites AND division and multiplication are opposites

Day 3: February 1st Objective: Understand the three rigid transformations (translations, reflections, and rotations) and learn some connections between them. Also, introduce notation for corresponding parts. THEN Begin to develop an understanding of reflection symmetry. Also, learn how to translate a geometric figure on a coordinate grid. Learn that reflection and reflection symmetry can help unlock relationships within a shape (isosceles triangle). Homework Check and Correct (in red) Try This! Problems 1-59 to 1-61 LL – “Rigid Transformations” Problems 1-68 to 1-72 Start Problems 1-87 to 1-89 (Notes if time) Homework: Problems 1-73 to 1-77 AND 1-82, 85, 86; GET SUPPLIES; Extra credit tissues or hand sanitizer

Try This! February 1st The distance along a straight road is measured as shown in the diagram below. If the distance between towns A and C is 67 miles, find the following: The value of x. The distance between A and B. 5x – 2 2x + 6 A B C 18

Transformation (pg 34) Transformation: A movement that preserves size and shape Reflection: Mirror image over a line Rotation: Turning about a point clockwise or counter clockwise Translation: Slide in a direction 19 19

Everyday Life Situations
Here are some situations that occur in everyday life. Each one involves one or more of the basic transformations: reflection, rotation, or translation. State the transformation(s) involved in each case. You look in a mirror as you comb your hair. While repairing your bicycle, you turn it upside down and spin the front tire to make sure it isn’t rubbing against the frame. You move a small statue from one end of a shelf to the other. You flip your scrumptious buckwheat pancakes as you cook them on the griddle. The bus tire spins as the bus moves down the road. You examine footprints made in the sand as you walked on the beach. 20

Day 4: February 2nd Objective: Begin to develop an understanding of reflection symmetry. Also, learn how to translate a geometric figure on a coordinate grid. Learn that reflection and reflection symmetry can help unlock relationships within a shape (isosceles triangle). THEN Learn about reflection, rotation, and translation symmetry. Identify which common shapes have each type of symmetry. Homework Check and Correct (in red) Finish Problems 1-70 to 1-72 LL – Notes Problems 1-87 to 1-89 Start Problem 1-97 if time Homework: Problems 1-92 to 1-96 AND 1-100; GET SUPPLIES; Extra credit tissues or hand sanitizer

1-71 Reflections Lines that connect corresponding points are ___________ to the line of reflection. The line of reflection ______ each of the segments connecting a point and its image. perpendicular bisects 22 22

1-72 B A A’ 23 23

Isosceles Triangle Sides: AT LEAST two sides of equal length
Base Angles: Have the same measure Height: Perpendicular to the base AND splits the base in half 24 24

1-72 Isosceles Triangles Two sides are _____ .
The ____ angles are equal. The line of reflection ______ the base. equal base bisects 25 25

Reflection across a Side
The two shapes MUST meet at a side that has the same length. 26 26

Polygons (pg 42) Polygon: A closed figure made up of straight segments. Regular Polygon: The sides are all the same length and its angles have equal measure.

Line: Slope-Intercept Form (pg 47)
y = mx + b Slope: Growth or rate of change. y-intercept: Starting point on the y-axis. (0,b) Slope y-intercept

First plot the y-intercept on the y-axis
Slope-Intercept Form Next, use rise over run to plot new points You can go backwards if you need! Now connect the points with a line! First plot the y-intercept on the y-axis

Parallel Lines (pg 47) Parallel lines do not intersect. Parallel lines have the same slope. For example: and

Perpendicular Lines (pg 47)
Perpendicular lines intersect at a right angle. Slopes of perpendicular lines are opposite reciprocals (opposite signs and flipped). For example: and

Day 5: February 3rd Objective: Begin to develop an understanding of reflection symmetry. Also, learn how to translate a geometric figure on a coordinate grid. Learn that reflection and reflection symmetry can help unlock relationships within a shape (isosceles triangle). THEN Learn about reflection, rotation, and translation symmetry. Identify which common shapes have each type of symmetry. Homework Check and Correct (in red) Wrap-Up Problem 1-89 LL – Notes Problem 1-98 Problems to 1-107 Homework: Problems to AND to 1-114; SUPPLIES; Chapter 1 Team Test Monday

Symmetry Symmetry: Refers to the ability to perform a transformation without changing the orientation or position of an object Reflection Symmetry: If a shape has reflection symmetry, then it remains unchanged when it is reflected across a line of symmetry. (i.e. “M” or “Y” with a vertical line of reflection) Rotation Symmetry: If a shape has rotation symmetry, then it can be rotated a certain number of degrees (less than 360°) about a point and remain unchanged. Translation Symmetry: If a shape has translation symmetry, then it can be translated and remain unchanged. (i.e. a line) 33

Venn Diagram #1: Has two or more siblings
#2: Speaks at least two languages

Venn Diagrams (pg 42) Condition #1 Condition #2 A B C D
Satisfies condition 2 only A B C Satisfies condition 1 only Satisfies neither condition Satisfies both conditions D

Problem 1-98(a) #1: Has at least one pair of parallel sides
#2: Has at least two sides of equal length

Problem 1-98(a) Has at least one pair of parallel sides Both
Has at least two sides of equal length Neither

Problem 1-98(b) Has only three sides Both Has a right angle Neither

Problem 1-98(c) Has reflection symmetry Both
Has 180° rotation symmetry Neither

Describing a Shape

Shape Toolkit

Day 6: February 6th Objective: Assess Chapter 1 in a team setting. THEN Develop an intuitive understanding of probability, and apply simple probability using the shapes in the Shape Bucket. Homework Check and Correct (in red) Try This! Algebra Review Chapter 1 Team Test Problems 1-115, 116, 119 Homework: Problems to AND CL1-126 to 1-129; Chapter 1 Individual Test Friday

Try This! February 6th Solve the following equations for x: 1. 2.

Probability (pg 60) Probability: a measure of the likelihood that an event will occur at random. Example: What is the probability of selecting a heart from a deck of cards?

Day 7: February 7th Objective: Develop an intuitive understanding of probability, and apply simple probability using the shapes in the Shape Bucket. THEN Learn how to name angles, and learn the three main relationships for angle measures, namely supplementary, complementary, and congruent. Also, discover a property of vertical angles. Homework Check and Correct (in red) Try This! Algebra Review Problems 1-116, 119 Problems 2-1 to 2-7 Homework: Problems CL1-130 to AND 2-8 to 2-11; Chapter 1 Individual Test Friday

Shape Bucket 47

2-2 A C’ C B B’

Notation for Angles Name Measure or Correct: Incorrect: ? ? F E D
If there is only one angle at the vertex, you can also name the angle using the vertex: Incorrect: Measure Correct: Incorrect: Y ? ? W X Z

Angle Relationships (pg 76)
Complementary Angles: Two angles that have measures that add up to 90°. Supplementary Angles: Two angles that have measures that add up to 180°. Example: Straight angle Congruent Angles: Two angles that have measures that are equal. Example: Vertical angles 30° x° 60° y° x° + y° = 90° 70° 110° x° y° x° + y° = 180° x° 85° y° x° = y° 85°

Day 8: February 8th Objective: Use our understanding of translation to determine that when a transversal intersects parallel lines, a relationship exists between corresponding angles. Also, continue to practice using angle relationships to solve for unknown angles. THEN Practice naming angles and stating angle relationships. Homework Check and Correct (in red) Distributive Property: Algebra Review Finish Problems 2-5 to 2-6 Problems 2-13 to 2-17 “Naming Angles 2” Worksheet Homework: Problems 2-18 to 2-22 Chapter 1 Individual Test Friday

Distributive Property
The two methods below multiply two expressions and rewrite a product into a sum. Note: There must be two sets of parentheses: ( x – 3 )2 = ( x – 3) ( x – 3 ) Box Method FOIL ( x + 5 )( x + 3 ) +5 x +5x +15 Firsts Outers Inners Lasts Simplify ( 3x – 2 )( 2x + 7) x2 +3x 6x2 + 21x + -4x + -14 = 6x2 + 17x – 14 x x2 + 8x + 15

Marcos’ Tile Pattern How can you create a tile pattern with a single parallelogram? 53 53

Marcos’ Tile Pattern Are opposite angles of a parallelogram congruent?
Pick one parallelogram on your paper. Use color to show which angles have equal measure. If two measures are not equal, make sure they are different colors. 54 54

Marcos’ Tile Pattern What does this mean in terms of the angles in our pattern? Color all angles that must be equal the same color. 55 55

Marcos’ Tile Pattern Are any lines parallel in the pattern? Mark all lines on your diagram with the same number of arrows to show which lines are parallel. 56 56

Marcos’ Tile Pattern J a L b M c d w N x P y z K Use the following diagram to help answer question 2-15. 57 57

Day 9: February 9th Objective: Use our understanding of translation to determine that when a transversal intersects parallel lines, a relationship exists between corresponding angles. Also, continue to practice using angle relationships to solve for unknown angles. THEN Practice naming angles and stating angle relationships. Homework Check and Correct (in red) Finish Problems 2-16 to 2-17 “Naming Angles 2” Worksheet Review Chapter 1 Team Test and Algebra Concepts Problems 2-23 to 2-25 More Chapter 1 Review if time Homework: Problems 2-29 to 2-33 Chapter 1 Individual Test TOMORROW

Why Parallel Lines? 53° x 59 59

2-16 X X

Day 10: February 10th Objective: Assess Chapter 1 in an individual setting. Silence your cell phone and put it in your school bag (not your pocket) Get a ruler, pencil/eraser, and calculator out First: Take the test Second: Check your work Third: Hand the test to Ms. Katz when you’re done Fourth: Correct last night’s homework Homework: Worksheet: “Angles and Parallel Lines” WILL BE COLLECTED AND GRADED ON CORRECTNESS ON MONDAY – SHOW WORK WHEN POSSIBLE!

Day 11: February 13th Objective: Apply knowledge of corresponding angles, and develop conjectures about alternate interior and same-side interior angles. Also, learn that when a light beam reflects off a mirror, the angle of the light hitting the mirror equals the angle of the light leaving the mirror. THEN Discover the triangle angle sum theorem, and practice finding angles in complex diagrams that use multiple relationships. Homework Check and Correct (in red) Problems 2-23 to 2-28 Problems 2-34 to 2-37 Conclusion Homework: Problems 2-38 to 2-42

2-23 (a) a a b

More Angles formed by Transversals
132° 48° > 48° 132° 132° 48° > 48° 132° a. Alternate Interior b. (1) Same Side Interior (2) (3)

Angles formed by Parallel Lines and a Transversal
Corresponding - Congruent Alternate Interior - Congruent Same-Side Interior - Supplementary b > > 100° a = b a > > 100° > > b 22° a = b a 22° > > > > b 60° a + b = 180° a 120° > >

Hands-On Activity Draw a large triangle (about 4 to 5 inches wide) using a ruler. Make sure that your triangle looks different than the other triangles in your group. Use scissors to cut out your triangle. Tear-off the angles of your triangle. Connect the three vertices of the torn angles

Triangle Angle Sum Theorem
The measures of the angles in a triangle add up to 180°. Example: B 45° 70° C 65° A

Day 12: February 14th Objective: Discover the triangle angle sum theorem, and practice finding angles in complex diagrams that use multiple relationships. THEN Learn the converses of some of the angle conjectures and see arguments for them. Also, apply knowledge of angle relationships to analyze the hinged mirror trick seen in Lesson THEN Learn how to find the area of a triangle and develop multiple methods to find the area of composite shapes formed by rectangles and triangles. Homework Check and Correct (in red) & Quick Warm-Up Finish Problems 2-35 to 2-37 Problems 2-43 to 2-48 Start Problems 2-66 to 2-69 Conclusion Homework: Problems 2-51 to 2-54 AND 2-62 to 2-65

Warm Up! February 14th Name the relationship between these pairs of angles: b and d a and x d and w c and w Possible Choices: x and y Vertical Angles Straight Angle Alternate-Interior Angles Corresponding Angles Same-side Interior Angles b a c d w x z y

2-37: Challenge! f g h 99° 123° m p 81° 57° q k 123° h k 57° 81° g 99°
42° r s r 57° 81° s v u 123° 57° u v 70

2-43 and 2-44 > x y >

2-43 and 2-44 A 100° B C 80° E D

2-43 and 2-44 > 112° 68° >

2-45 80° > > 100° 80° 100° 80° 80° > >
If Same-Side Interior angles are supplementary, then the lines must be parallel. If Corresponding angles are congruent, If Alternate Interior angles are congruent, then the lines must be parallel. then the lines must be parallel.

Day 13: February 15th Objective: Learn how to find the area of a triangle and develop multiple methods to find the area of composite shapes formed by rectangles and triangles. THEN Use rectangles and triangles to develop algorithms to find the area of new shapes, including parallelograms and trapezoids. Homework Check and Correct (in red) & Quick Warm-Up Problems 2-66 to 2-69 Problems 2-75 to 2-79 Conclusion Homework: Problems 2-70 to 2-74 AND 2-81 to 2-85

Area of a Right Triangle
What is the area of the right triangle below? Why? What about non-right triangles? 4 cm 10 cm

Where is the Height & Base
77

Obtuse Triangle Height Extra Base
Area of Obtuse Triangle = Area of Right Triangle = ½ (Base)(Height) 78

Area of a Triangle The area of a triangle is one half the base times the height. Height Height Height Base Base Base

Day 14: February 16th Objective: Use rectangles and triangles to develop algorithms to find the area of new shapes, including parallelograms and trapezoids. THEN Explore how to find the height of a triangle given that one side has been specified as the base. Additionally, find the areas of composite shapes using the areas of triangles, parallelograms, and trapezoids. Homework Check and Correct (in red) & Warm-Up! Problems 2-75 to 2-79 Problems 2-86 to 2-89 Conclusion Homework: Problems 2-90 to 2-94 Optional E.C: Do Problem 2-49 on a separate sheet of paper and hand it in on Monday. It must be neat and well- explained to be considered for credit.

Warm-Up! February 16th Answer the following questions:
The area of a triangle is 40 in2 and the base is 8 inches. What is the length of the height? Find the value of x in the figure below if the area of the triangle is 60 in2. 2x + 1 8 in

Can We find the Area? YES! YES! YES! YES! YES! YES! YES! YES!

Area of a Parallelogram
h Height h Base h b h Area = b.h Rectangle!

h b Area = b.h

The area of a parallelogram is the base times the height. Ex: Area = b.h h b 20 13 5 13 A = 20.5 = 100 20 85

Area = (b1 + b2) h Reflect Parallelogram! Duplicate Translate
Area of a Trapezoid b2 b1 b1 Base One b2 h h Height h b2 b1 b2 Base Two b1 Area = (b1 + b2) h Reflect Parallelogram! Duplicate Translate

Area of a Trapezoid b1 h b2 Area =

Area = Area of a Trapezoid
The area of a trapezoid is half of the sum of the bases times the height. Ex: b1 Area = h b2 9 5 5 A = ½ (9+15) 4 = ½ = 48 4 15 88

Answers to 2-79 0.5(16)9 = 72 sq. un 26(14) = 364 sq. un

Day 15: February 17th Objective: Explore how to find the height of a triangle given that one side has been specified as the base. Additionally, find the areas of composite shapes using the areas of triangles, parallelograms, and trapezoids. THEN Review the meaning of square root. Also, recognize how a square can help find the length of a hypotenuse of a right triangle. Homework Check and Correct (in red) & Warm-Up! Problems 2-86 to 2-89 Problems 2-95 to 2-97 Conclusion Homework: Problems to (Skip 101) Optional E.C: Do Problem 2-49 on a separate sheet of paper and hand it in on Monday. It must be neat and well- explained to be considered for credit.

Warm Up! February 17th Solve for x in both diagrams -(x – 36°) >
7 + 4x units > 2x + 9° 7 units The area of the polygon above is 357 un2.

Note card = Height Locator
Base “Weight”

Day 16: February 21st Objective: Review the meaning of square root. Also, recognize how a square can help find the length of a hypotenuse of a right triangle. THEN Learn how to determine whether or not three given lengths can make a triangle. Also, understand how to find the maximum and minimum lengths of a third side given the lengths of the other two sides. Homework Check and Correct (in red) & Collect Optional E.C. Quick Warm-Up! Problems 2-96 to 2-97 Problems 2-105, to 2-108 Conclusion Homework: Problems to 2-113 Chapter 2 Team Test Tomorrow [Review transformations and angle relationship vocabulary]

Warm Up! February 21st Solve the 2 equations for x. Are there more solutions not listed? x2 = [A] [B] 5.29 [C] 28 [D] 5 x2 + 9 = 130 [A] [B] 11 [C] 8.40 [D] 121

Day 17: February 22nd Objective: Assess Chapter 2 in a team setting. THEN Learn how to determine whether or not three given lengths can make a triangle. Also, understand how to find the maximum and minimum lengths of a third side given the lengths of the other two sides. Homework Check and Correct (in red) Chapter 2 Team Test Problems 2-105, to 2-108 Conclusion Homework: Problems to 2-122 Chapter 2 Individual Test Tuesday

Pink Slip Can these three side lengths form a triangle? Why? 12, 4, 8
13, 10, 5 11, 9, 30 96

Triangle Inequality a – c < b < a + c b – c < a < b + c
Each side must be shorter than the sum of the lengths of the other two sides and longer than the difference of the other two sides. a – b < c < a + b a – c < b < a + c b – c < a < b + c b a c

Triangle Inequality Longest Side: Slightly less than the sum of the two shorter sides Shortest Side: Slightly more than the difference of the two shorter sides

Day 18: February 23rd Objective: Learn how to determine whether or not three given lengths can make a triangle. Also, understand how to find the maximum and minimum lengths of a third side given the lengths of the other two sides. THEN Develop and prove the Pythagorean Theorem. Homework Check and Correct (in red) Finish Problems 2-105, to 2-108 Problems to 2-117 Conclusion Homework: Problems CL2-123 to 2-131 Chapter 2 Individual Test Tuesday

The Pythagorean Theorem
b c a b c a b c a b c b2 a b c a b c c2 a b c a b c a2 a2 + b2 = c2

a2 + b2 = c2 Pythagorean Theorem Hypotenuse Leg Leg B a c C A b
When to use it: If you have a right triangle You need to solve for a side length If two sides lengths are known

Practice Problem Solve for x Do you need to solve for a side or angle?
Do you have two sides or a side and an angle? 6 in 7 in Pythagorean Theorem

Practice Problem Solve for x Do you need to solve for a side or angle?
Do you have two sides or a side and an angle? 9 m 5 m x Pythagorean Theorem

Day 19: February 24th Objective: Learn the concept of similarity and investigate the characteristics that figures share if they have the same shape. Determine that two geometric figures must have equal angles to have the same shape. Additionally, introduce the idea that similar shapes have proportional corresponding side lengths. Homework Check and Correct (in red) Review Chapter 2 Team Test Problems 3-1 to 3-5 Time? More Chapter 2 Review Time Conclusion Homework: Problems 3-5 to 3-10 Chapter 2 Individual Test Tuesday

Dilation A transformation that shrinks or stretches a shape proportionally in all directions.

Enlarging

Day 20: February 27th Objective: Determine that multiplying (and dividing) lengths of shapes by a common number (zoom factor) produces a similar shape. Use the equivalent ratios to find missing lengths in similar figures and learn about congruent shapes. THEN Examine the ratio of the perimeters of similar figures, and practice setting up and solving equations to solve proportional problems. Homework Check and Correct (in red) & Warm-Up! Review Problems 3-5 and 3-10 and Terms: “Dilation” and “Similar” Problems 3-11 to 3-15 Start Problems 3-22 to 3-25 Conclusion Homework: Problems 3-17 to 3-21 AND STUDY Chapter 2 Individual Test Tomorrow

Do this in your graph notebook:
A triangle has the following coordinates: (-3,4), (2,4), and (2,-1) Plot and connect the points on a graph that goes from -10 to 10 on both axes. Find the area of the triangle. Find the length of the hypotenuse. Find the perimeter.

Chapter 1-2 Topics Angles:
Acute, Obtuse, Right, Straight, Circular – p. 24 Complementary, Supplementary, Congruent – p. 76 Vertical, Corresponding, Same-Side Interior, Alternate Interior – Toolkit and p. 91 Lines: Slopes of parallel and perpendicular lines – p. 47 Transformations: Reflection, Rotation, Translation, and Prime Notation – p.81 Shapes: Name/Define shapes – Toolkit Probability: Use proper notation…Ex: P(choosing a King) = 4/52 = 1/13 Page 60 109

Chapter 1-2 Topics Triangles: Triangle Angle Sum Theorem – p.100 Area
Triangle Inequality Theorem Area: Triangle, Parallelogram, Rectangle, Trapezoid, Square Page 112 and Learning Log/Toolkit Pythagorean Theorem & Square Roots – p. 115 and 123 110

Exactly same shape but not necessarily same size
Similar Figures Exactly same shape but not necessarily same size Corresponding Angles are congruent The ratios between corresponding sides are equal 21 127° 90° 7 15 127° 90° 5 12 4 53° 90° 53° 90° 10 30

The number each side is multiplied by to enlarge or reduce the figure
Zoom Factor The number each side is multiplied by to enlarge or reduce the figure Example: Zoom Factor = 2 x2 x2 3 18 9 x2 12 24 6

Notation Angle ABC Line Segment XY The Measure of Angle ABC
The Length of line segment XY

Notation Acceptable Not Acceptable

Day 21: February 28th Objective: Assess Chapter 2 in an individual setting. Silence your cell phone and put it in your school bag (not your pocket) Get a ruler, pencil/eraser, and calculator out First: Take the test Second: Check your work Third: Hand the test to Ms. Katz when you’re done Fourth: Correct last night’s homework Homework: Problems 3-27 to 3-31

Day 22: February 29th Objective: Examine the ratio of the perimeters of similar figures, and practice setting up and solving equations to solve proportional problems. THEN Apply proportional reasoning and learn how to write similarity statements. Homework Check and Correct (in red) Review Problem 3-29 as a class Finish Problems 3-22 to 3-25 Problems 3-32 to 3-37 Conclusion Homework: Problems 3-38 to 3-42

Notation Angle ABC Line Segment XY The Measure of Angle ABC
The Length of line segment XY

Notation Acceptable Not Acceptable

George Washington’s Nose
60 ft ? in ? ft ? in ? ft ? ft ? in

Day 23: March 1st Objective: Apply proportional reasoning and learn how to write similarity statements. THEN Learn the SSS~ and AA~ conjectures for determining triangle similarity. Homework Check and Correct (in red) Finish Problems 3-32 to 3-37 Problem 3-43 Conclusion Homework: Problems 3-48 to (SKIP 3-49)

Writing a Similarity Statement
Example: ΔDEF~ΔRST The order of the letters determines which sides and angles correspond. B Z C Y A X Δ A A BC BC Δ Z Z XY XY ~ 122 122

Writing a Proportion 25 s 13 10 AB ABCD ~ WXYZ BC WX XY AB AB WX WX =
123 123

Day 24: March 5th Objective: Apply proportional reasoning and learn how to write similarity statements. THEN Learn the SSS~ and AA~ conjectures for determining triangle similarity. Homework Check and Correct (in red) Review of Classroom Expectations Finish Problems 3-35 to 3-37 Problems 3-43 to 3-47 Review Chapter 2 Individual Test Conclusion Homework: Problem 3-49, AND Worksheet #2,3,6,7,8 – Show work! [Worksheet will be collected and graded on accuracy.]

Warm Up! March 5th The figures are drawn to scale and are similar, find the length of x and y: Figure ABCD is similar to WXYZ. Find the length of z: 15 W 18 A B Z 8 10 6 z 12 X x Y D C 3 y

First Two Similarity Conjectures
SSS Triangle Similarity (SSS~) If all three corresponding side lengths share a common ratio, then the triangles are similar. AA Triangle Similarity (AA~) If two pairs of angles have equal measure, then the triangles are similar.

Day 25: March 6th Objective: Learn the SSS~ and AA~ conjectures for determining triangle similarity. THEN Learn how to use flowcharts to organize arguments for triangle similarity, and continue to practice applying the AA~ and SSS~ conjectures. Homework Check and Correct (in red) Finish Problems 3-46 to 3-47 Problems 3-53 to 3-58 Start Problems 3-64 to 3-67 Conclusion Homework: Problems 3-59 to 3-63 (Can skip 3-62)

Warm-Up! The Triangles are Similar
Find PT and PR: Find the length of y: 4 6 y 9

Similarity and Sides The following is not acceptable notation: OR

3-54 What Conjecture will we use: SSS~ SSS~ Facts Conclusion
D T 3 16 C 4 12 Q 2 8 F R What Conjecture will we use: SSS~ Facts Conclusion ΔCDF ~ ΔRTQ SSS~

Another Example What Conjecture will we use: AA~ AA~ Facts Conclusion
Y B 100° 100° A 60° 60° C X Z What Conjecture will we use: AA~ Facts Conclusion ΔABC ~ ΔZYX AA~

Day 26: March 7th Objective: Practice making and using flowcharts in more challenging reasoning contexts. Also, determine the relationship between two triangles if the common ratio between the lengths of their corresponding sides is 1. THEN Complete the list of triangle similarity conjectures involving sides and angles, learning about the SAS~ Conjecture in the process. Homework Check and Correct (in red) Warm-Up! Wrap-Up Problem 3-58 (LL Entry and Math Notes) Problems 3-64 to 3-67 Start Problems 3-73 to 3-77 Conclusion Homework: Problems 3-68 to 3-72 Chapter 3 Team Test Friday

Warm Up! March 7th Decide if the triangles (not drawn to scale) below are similar. Use a flowchart to organize your facts and conclusion. O A 18 27 S 20 12 45 N T B 8

Day 27: March 8th Objective: Complete the list of triangle similarity conjectures involving sides and angles, learning about the SAS~ Conjecture in the process. THEN Practice using the three triangle similarity conjectures and organizing reasoning in a flowchart. Homework Check and Correct (in red) Warm-Up! Finish Problem 3-66 Finish Problems 3-66 to 3-67 Problems 3-73 to 3-77 Problem 3-83 Conclusion Homework: Problems 3-78 to 3-82 Chapter 3 Team Test Tomorrow

Conditions for Triangle Similarity
If you are testing for similarity, you can use the following conjectures: SSS~ All three corresponding side lengths have the same zoom factor AA~ Two pairs of corresponding angles have equal measures. SAS~ Two pairs of corresponding lengths have the same zoom factor and the angles between the sides have equal measure. NO CONJECTURE FOR ASS~ 14 6 7 3 10 5 55° 40° 40° 55° 40 20 70° 70° 30 15

Day 28: March 9th Objective: Practice using the three triangle similarity conjectures and organizing reasoning in a flowchart. THEN Assess Chapter 3 in a team setting. Homework Check and Correct (in red) Warm-Up! Start Problem 3-85 Problems 3-85 to 3-86 Chapter 3 Team Test Time? Problem 3-93 (Interesting mirror activity) Conclusion Homework: Problems 3-88 to 3-92 Chapter 3 Individual Test Thursday

You’re Getting Sleepy…
Eye Height Eye Height x cm 200 cm

Day 29: March 12th Objective: Practice using the three triangle similarity conjectures and organizing reasoning in a flowchart. THEN Review Chapters 1-3. Homework Check and Correct (in red) Problem 3-94 Chapter 1-3 Topics Problems CL3-101 to CL3-105 Conclusion Homework: Problems 3-96 to AND CL3-107 to CL3-110 Chapter 3 Individual Test Thursday

Lessons from Abroad x 316 ft = 942 6 – 2 = 4 12

Chapter 1-2 Topics Angles:
Acute, Obtuse, Right, Straight, Circular – p. 24 Complementary, Supplementary, Congruent – p. 76 Vertical, Corresponding, Same-Side Interior, Alternate Interior – Toolkit and p. 91 Lines: Slopes of parallel and perpendicular lines – p. 47 Transformations: Reflection, Rotation, Translation, and Prime Notation – p.81 Shapes: Name/Define shapes – Toolkit Probability: Use proper notation…Ex: P(choosing a King) = 4/52 = 1/13 Page 60 140

Chapter 1-2 Topics Triangles: Triangle Angle Sum Theorem – p.100 Area
Triangle Inequality Theorem Area: Triangle, Parallelogram, Rectangle, Trapezoid, Square Page 112 and Learning Log/Toolkit Pythagorean Theorem & Square Roots – p. 115 and 123 141

Chapter 3 Topics Dilations Zoom Factor – p. 142 Similarity
Writing similarity statements – p.150 Triangle Similarity Statements: AA~, SSS~, SAS~ Page 155 and 171 Flowcharts Congruent Shapes – p. 159 Solving Quadratic Equations – p. 163 142

Day 30: March 13th Objective: Recognize that all slope triangles on a given line are similar to each other, and begin to connect a specific slope to a specific angle measurement and ratio. Homework Check and Correct (in red) & Warm-Up! Quick Team Tests Start Problems 4-1 to 4-5 Conclusion Homework: Problems 4-6 to 4-10 Chapter 3 Individual Test Thursday

[Perhaps use x-values from -5 to 5?]
Warm Up! March 13th 1. Make a table in order to graph the following equation: [Perhaps use x-values from -5 to 5?] 2. Factor the following equation in order to solve for x:

Day 31: March 14th Objective: Recognize that all slope triangles on a given line are similar to each other, and begin to connect a specific slope to a specific angle measurement and ratio. Homework Check and Correct (in red) Problems 4-2 to 4-5 Conclusion Homework: Angles Puzzle Worksheet Chapter 3 Individual Test Tomorrow

Day 32: March 15th Objective: Assess Chapter 3 in an individual setting. Silence your cell phone and put it in your school bag (not your pocket) Get a ruler, pencil/eraser, and calculator out First: Take the test Second: Check your work! Third: Hand the test to Ms. Katz when you’re done Fourth: Correct last night’s homework & sit quietly Homework: Enjoy one free night from math homework!

Day 33: March 16th Objective: Connect specific slope ratios to their related angles and use this information to find missing sides or angles of right triangles with 11°, 22°, 18°, or 45° angles (and their complements). THEN Use technology to generate slope ratios for new angles in order to solve for missing side lengths on triangles. Homework Check and Correct (in red) Problems 4-11 to 4-15 Start Problems 4-21 to 4-24 Conclusion Homework: Problems 4-16 to 4-20

Day 34: March 19th Objective: Use technology to generate slope ratios for new angles in order to solve for missing side lengths on triangles. THEN Practice using slope ratios to find the length of a leg of a right triangle and learn that this ratio is called tangent. Also, practice re-orienting a triangle and learn new ways to identify which leg is Δx and which is Δy. Homework Check and Correct (in red) & Warm-Up! Finish Problems 4-22 to 4-24 Problems 4-30 to 4-35 Conclusion Homework: Problems 4-25 to 4-29 (Skip 28) AND Problems 4-36 to 4-40 (Skip 39)

Warm-Up! March 19th Solve for x hypotenuse x 68° 25 cm

Day 35: March 20th Objective: Practice using slope ratios to find the length of a leg of a right triangle and learn that this ratio is called tangent. Also, practice re-orienting a triangle and learn new ways to identify which leg is Δx and which is Δy. THEN Apply knowledge of tangent ratios to find measurements about the classroom. Homework Check and Correct (in red) & Warm-Up! Finish Problems 4-34 to 4-35 Problems 4-41 to 4-42 Review Chapter 3 Individual Test Conclusion Homework: Problems 4-43 to 4-47

Trigonometry Theta ( ) is always an acute angle Opposite
(across from the known angle) Hypotenuse (across from the ° angle) h Δy Δx Adjacent (forms the known angle)

Trigonometry Theta ( ) is always an acute angle Opposite
(across from the known angle) Hypotenuse (across from the ° angle) h o a Adjacent (forms the known angle)

Theta ( ) is always an acute angle
Trigonometry (LL) Theta ( ) is always an acute angle h Opposite Adjacent

Theta ( ) is always an acute angle
Trigonometry (LL) Theta ( ) is always an acute angle h Adjacent Opposite

Day 36: March 21st Objective: Review the tangent ratio. THEN Learn how to list outcomes systematically and organize outcomes in a tree diagram. THEN Continue to use tree diagrams and introduce a table to analyze probability problems. Also, investigate the difference between theoretical and experimental probability. Homework Check and Correct (in red) & Warm-Ups! Review Tangent (Practice Problems) Problems 4-49 to 4-53 Problem 4-59 Conclusion Homework: Problems 4-54 to 4-58 Chapter 4 Team Test Friday

Warm Up! March 20th Find the length of x:
If a bag contains 6 yellow, 10 red, and 8 green marbles. What is the probability of selecting a red marble at random. 9 7 x 4

Warm Up! March 21st Multiply the following expressions using an area diagram: 1. 2.

When to use Trigonometry
You have a right triangle and… You need to solve for a side and… A side and an angle are known Use Trigonometry

Take Bus #41 and Listen to an MP3 player
My Tree Diagram Read Write #41 #41 Listen Listen START Read #28 Write Listen #55 Read Write One Possibility: Take Bus #41 and Listen to an MP3 player #81 Listen Read Write Listen 159

Day 37: March 22nd Homework Check and Correct (in red) & Warm-Ups!
Objective: Continue to use tree diagrams and introduce a table to analyze probability problems. Also, investigate the difference between theoretical and experimental probability. THEN Learn how to use an area model (and a generic area model) to represent a situation of chance. Homework Check and Correct (in red) & Warm-Ups! Problem 4-60 Problems 4-68 to 4-70 Problems 4-77 to 4-78 Conclusion Homework: Problems 4-63 to 4-67 AND 4-72 to 4-74 Chapter 4 Team Test Tomorrow Problem 4-71 can be counted for E.C. – see Ms. Katz for a worksheet. (Complete individually – if I think you shared/copied, no points will be awarded.) Due Monday

Warm Up! March 22nd Multiply the following expressions using an area diagram: 1. 2.

Warm Up! March 22nd Solve for x and y: 60° x y 6 6 · · 6

4-60: Tree Diagram $100 $300 $1500 START Keep $100 Double $200 Keep
$600 $1500 Keep $1500 Double $3000 163

Day 38: March 23rd Objective: Learn how to use an area model (and a generic area model) to represent a situation of chance. THEN Assess Chapter 4 in a team setting. Homework Check and Correct (in red) & Warm-Up! Finish Problem 4-77 Chapter 4 Team Test Problems 4-78 to 4-80 Math Notes Box – Notes in LL Conclusion Homework: Problems 4-75 to 4-76 AND 4-82 to 4-86 Chapter 4 Individual Test Next Friday Problem 4-71 can be counted for E.C. – see Ms. Katz for a worksheet. (Complete individually – if I think you shared/copied, no points will be awarded.) Due Monday

4-77: Area Diagram Spinner #1 I U A IT UT AT T Spinner #2 IF UF AF F

Warm-Up! March 23rd Make an area diagram to model the game where both spinners below are used. Then find the probabilities below: P(A, X) = P(C, Y) = P(not A, Y) = A B X Y B C

Day 39: March 26th Objective: Develop more complex tree diagrams to model biased probability situations. THEN Review Chapter 4 by working through closure problems. ***NEW SEATS*** Homework Check and Correct (in red) & Collect Optional E.C. Warm-Up! Problems 4-78 to 4-80 and Math Notes Box – Notes in LL Review Chapter 4 Team Test Problems CL4-96 to CL4-105 Conclusion Homework: Problems 4-91 to 4-95 AND CL4-100 to CL4-105 Chapter 4 Individual Test Friday [If you know you’re not going to be here due to extenuating circumstances, you must see me ahead of time to take the test.]

Warm-Up! March 26th Use an area model or tree diagram to answer these questions based on the spinners below: If each spinner is spun once, what is the probability that both spinners show blue? If each spinner is spun once, what is the probability that both spinners show the same color? If each spinner is spun once, what is the probability of getting a red-blue combination?

Day 40: March 27th Objective: Review Chapter 4 by working through closure problems. THEN Learn about the sine and cosine ratios, and start a Triangle Toolkit. Homework Check and Correct (in red) Warm-Up! Slide and Do Problems CL4-96 to 4-99 Problems 5-1 to 5-6 Conclusion Homework: Problems 5-7 to 5-11 Chapter 4 Individual Test Friday [If you know you’re not going to be here due to extenuating circumstances, you must see me ahead of time to take the test.]

Warm-Up! March 27th Solve for the length of x and y: h y o 10 cm x a
Step 1: h y o 10 cm Step 2: 71° x a

Chapter 4 Topics Slope Angles/Ratios: Trigonometry:
Tangent Ratio – p. 200 Use tangent to solve for a missing side of a slope triangle As the slope angle increases, does the slope ratio increase or decrease? (Look at yellow Trig Table) Problems like the Leaning Tower of Pisa, Statue of Liberty, etc (Clinometer activities) Probability: Tree Diagrams Area Models Equally likely events (like the bus problem) Biased events (like Problem 4-69 and 4-77) Math Notes on Page 219 171

Day 41: March 28th Objective: Learn about the sine and cosine ratios, and start a Triangle Toolkit. THEN Develop strategies to recognize which trigonometric ratio to use based on the relative position of the reference angle and the given sides involved. Homework Check and Correct (in red) Warm-Up! Problems 5-5 to 5-6 Problems 5-12 to 5-15 Conclusion Homework: Problems 5-16 to 5-20 Chapter 4 Individual Test Friday [If you know you’re not going to be here due to extenuating circumstances, you must see me ahead of time to take the test.]

Warm-Up! March 28th Find the area of the triangle: h o 6 cm 30° a or

Trigonometry SohCahToa h o a

Day 42: March 29th Objective: Develop strategies to recognize which trigonometric ratio to use based on the relative position of the reference angle and the given sides involved. THEN Use sine, cosine, and tangent ratios to solve real world application problems. Homework Check and Correct (in red) Warm-Up! Finish Problems 5-12 to 5-15 Problems 5-31 to 5-33 Conclusion Homework: Problems 5-36 to 5-40 Chapter 4 Individual Test Tomorrow – STUDY!

Warm-Up! March 29th Are the following triangles similar? If so, make a flowchart. If not, explain why they are not similar and/or what information is missing. 1. 2.

Day 43: March 30th Objective: Assess Chapter 4 in an individual setting. Silence your cell phone and put it in your school bag (not your pocket) Get a ruler, pencil/eraser, and calculator out First: Take the test Second: Check your work Third: Give test & formula sheet to Ms. Katz when you’re done Fourth: Correct last night’s homework Homework: Problems 5-26 to 5-30 Enjoy your week away from school!

*Beginning of Quarter 4*
Day 44: April 10th Objective: Review previous material. THEN Understand how to use trig ratios to find the unknown angle measures of a right triangle. Also, introduce the concept of “inverse.” *Beginning of Quarter 4* Homework Check and Correct (in red) Review Chapter 4 Test in detail Trig Practice WS - #1, 2, 3, 4, 9, 11, 13 Problems 5-21 to 5-25 Conclusion Homework: Problems #5, 6, 7, 8, 10, 12, 14 on WS

Day 45: April 11th Objective: Understand how to use trig ratios to find the unknown angle measures of a right triangle. Also, introduce the concept of “inverse.” THEN Recognize the similarity ratios in 30°-60°-90° and 45°-45°-90° triangles and begin to apply those ratios as a shortcut to finding missing side lengths. Homework Check and Correct (in red) Finish Problems 5-21 to 5-25 Trig/Inverse Trig Practice Worksheet Problems 5-41 to 5-45 Conclusion Homework: Problems 5-46 to 5-50 (skip 49)

When to use Inverse Trig
You have a right triangle and… You need to solve for a angle and… Only two sides are known Use Inverse Trigonometry

The square of whole numbers.
Perfect Squares The square of whole numbers. 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 , 121, 144 , 169 , 196 , 225, etc

Simplifying Square Roots
Check if the square root is a whole number Find the biggest perfect square (4, 9, 16, 25, 36, 49, 64) that divides the number Rewrite the number as a product Simplify by taking the square root of the number from (2) and putting it outside CHECK! Note: A square root can not be simplified if there is no perfect square that divides it. ex: √15 , √21, and √17 Just leave it alone.

Simplifying Square Roots
Write the following as a radical (square root) in simplest form:

Day 46: April 12th Objective: Recognize the similarity ratios in 30°-60°-90° and 45°-45°-90° triangles and begin to apply those ratios as a shortcut to finding missing side lengths. THEN Learn to recognize 3:4:5 and 5:12:13 triangles and find other examples of Pythagorean triples. Additionally, practice recognizing and applying all three of the new triangle shortcuts. Homework Check and Correct (in red) Problems 5-43 to 5-45 Review HW Problem 5-46 Problems 5-51 to 5-55 Conclusion Homework: Problems 5-56 to 5-60

Warm-Up! April 12th Solve for the measures of x and y: a o 10 in a o

You can use this whenever a problem has an equilateral triangle!
30° – 60° – 90° A 30° – 60° – 90° is half of an equilateral (three equal sides) triangle. You can use this whenever a problem has an equilateral triangle! 30° s 60° .5s s

30° – 60° – 90° 30° Hypotenuse Long Leg (LL) 60° Short Leg (SL)

30° – 60° – 90° Remember √3 because there are 3 different angles You MUST know SL first! 30° 2 √3 ÷2 60° 1 ÷√3 SL LL Hyp x√3 x2

Isosceles Right Triangle 45° – 45° – 90°
Remember √2 because 2 angles are the same 45° √2 1 45° ÷√2 1 Leg(s) Hypotenuse x√2

Isosceles Right Triangle 45° – 45° – 90°
A 45° – 45° – 90° triangle is half of a square. You can use this whenever a problem has a square with its diagonal! 45° d s 45° s

Day 47: April 13th Objective: Learn to recognize 3:4:5 and 5:12:13 triangles and find other examples of Pythagorean triples. Additionally, practice recognizing and applying all three of the new triangle shortcuts. THEN Review tools for finding missing sides and angles of triangles, and develop a method to solve for missing sides and angles for a non-right triangle. Homework Check and Correct (in red) Problems 5-51 to 5-55 Problems 5-61 to 5-65 Conclusion Homework: Problems 5-67 to 5-72 Ch. 5 Team Test Wednesday Midterm Exam Friday (?)

Pythagorean Triple A Pythagorean triple consists of three positive integers a, b, and c (where c is the greatest) such that: a2 + b2 = c2 Common examples are: 3, 4, 5 ; 5, 12, 13 ; and 7, 24, 25 Multiples of those examples work too: 3, 4, 5 ; 6, 8, 10 ; and 9, 12, 15

Day 48: April 16th Objective: Recognize the relationship between a side and the angle opposite that side in a triangle. Also, develop the Law of Sines, and use it to find missing side lengths and angles of non-right triangles. Homework Check and Correct (in red) Review Math Notes prior to Problem 5-67 Problems 5-73 to 5-76 Conclusion Homework: Problems 5-79 to 5-84 Ch. 5 Team Test Wednesday Midterm Exam Friday (?)

Day 49: April 17th Objective: Complete the Triangle Toolkit by developing the Law of Cosines. THEN Review tools for solving for missing sides and angles of triangles. Homework Check and Correct (in red) Warm-Up! Problems 5-85 to 5-87 Problem 5-98 Conclusion Homework: Problems 5-89 to 5-94 (Skip 5-91) Ch. 5 Team Test Tomorrow Midterm Exam Friday (?)

Warm-Up! April 17th The angles of elevation to an airplane from two people on level ground are 55° and 72°, respectively. The people are facing the same direction and are 2.2 miles apart. Find the altitude (height) of the plane. Diagram: Solve: h 55° 72° 2.2 mi Solution/Answer: The airplane is about 5.87 miles above the ground.

Day 50: April 18th Objective: Review tools for solving for missing sides and angles of triangles. THEN Assess Chapter 5 in a team setting. Homework Check and Correct (in red) Warm-Up! Do Problems 5-98 and 5-122 Chapter 5 Team Test Conclusion Homework: Problems to & Work on Triangle Review WS Midterm Exam Friday (?)

Day 51: April 19th Objective: Review and practice Chapter 1-5 topics.
Homework Check and Correct (in red) Problems 5-98(a), to 5-109 Problems CL5-126 to 5-130, 5-133, and Check Conclusion Homework: Worksheets: “Special Right” – Left side on the front (4 problems) “Law of Sines and Cosines” – ODDS (front & back) Midterm Exam Friday

Day 52: April 20th Objective: Review and practice Chapter 1-5 topics.
Homework Check Review Homework Worksheets Problem 5-114 Practice Problems Triangle Review Worksheet (some of you already have it) Conclusion Homework: Problems to AND 5-124 Midterm Exam Wed. and Thurs.

Chapter 5 Topics Trigonometry:
Tangent, Sine, and Cosine Ratios – p. 241 Inverse Trigonometry – p. 248 Special Right Triangles: –p. 260 and LL –p. 260 and LL Pythagorean Triples – p. 260 Non-Right Triangle Tools: Law of Sines – p. 264 and LL Law of Cosines – p. 267 and LL 199

Algebraic Triangle Angle Sum
2x – 13° 2x + 4° x + 24° A B Extra Practice

The Triangle Inequality
Which of the following lengths can form a triangle? Which of the following lengths cannot form a triangle? I. 5, 9, 20 II. 6, 10, 13 III. 7, 8, 14 IV. 15, 21, 36 No 5+9<20 20–9>5 Yes 6+10>13 13–10<6 Yes 7+8>14 14–8<7 No 15+21=36 36–21=15 Extra Practice

Area of a Triangle What is the area of the shaded region? 8 units
Extra Practice

Similarity Based on Statements
7 E EF AC 11 = DF BC A 8 C x x 8 = 25 11 D 25 F Extra Practice

Probability A T Greg is going to flip a coin twice. What is the probability heads will not come up? First Flip T ( ½ ) H ( ½ ) START T TT TH HT HH T H H ( ½ ) T ( ½ ) Second Flip T H H Probability Extra Practice

Rotation in a Coordinate Grid
Rotate the point (-4,5) either 90° or 180° (-4,5) (5,4) (-5,-4) (4,-5) Extra Practice

Angle Measures in Right Triangles
Find the measure of angle A to the nearest degree: A B 26 24 C

Transformations: Rotation
Rotate ΔABC counter-clockwise around the origin. What are the coordinates of A’? C B A C B A

Angle Relationships: Equations
Solve for x:

Area: Trapezoid Find the area of the trapezoid: 15 in. 10 in. 20 in.

Area and Lengths: Triangle
The area of ΔABC is 60 sq. inches. What is the length of segment KC? B 10 in. 8 in. A C K

Algebraic Areas: Square
Find the perimeter and area of the square below:

Day 53: April 23rd Objective: Practice identifying congruent triangles by first determining that the triangles are similar and that the ratio of corresponding sides is 1. Homework Check Problems 6-1 to 6-3 Conclusion Homework: Problems 6-4 to 6-9 (Skip 6-8) AND STUDY! (Remember: You need to know Laws of Sines & Cosines!) Midterm Exam Wed. and Thurs.

*MULTIPLE CHOICE #1-18 ONLY TODAY*
Day 54: April 25th Objective: Assess Chapters 1-5 in an individual setting. *MULTIPLE CHOICE #1-18 ONLY TODAY* Silence your cell phone and put it in your school bag (not your pocket) Get a ruler, pencil/eraser, and calculator out First: Take the test Second: Check your work Third: Give test & formula sheet to Ms. Katz when you’re done Fourth: Correct last night’s homework Work on Problem 6-2 with Ms. Katz Homework: Problems 6-13 to 6-18

*MULTIPLE CHOICE #19-25 AND OPEN-ENDED*
Day 55: April 26th Objective: Assess Chapters 1-5 in an individual setting. *MULTIPLE CHOICE #19-25 AND OPEN-ENDED* Silence your cell phone and put it in your school bag (not your pocket) Get a ruler, pencil/eraser, and calculator out First: Take the test Second: Check your work Third: Give test & formula sheet to Ms. Katz when you’re done Fourth: Correct last night’s homework Work on Problem 6-3 with Ms. Katz Start Problems 6-10 to 6-12 Homework: Problems 6-24 to 6-29

Day 56: April 27th Homework: Problems 6-43 to 6-48
Objective: Use understanding of similarity and congruence to develop triangle congruence shortcuts. THEN Extend the use of flowcharts to document triangle congruence facts. Practice identifying pairs of congruent triangles and contrast congruence arguments with similarity arguments. Homework Check and Correct (in red) Problems 6-11 to 6-12 Problems 6-19 to 6-23 Conclusion Homework: Problems 6-43 to 6-48 Ch. 6 Team Test Monday Ch. 6 Individual Test Friday Is your book damaged? Torn/missing pieces of book cover means that your book needs to be replaced. Bring cash or check for $19 ASAP. If you think it can be repaired, see Ms. Katz – do NOT make a mess of it with tape! You will be getting Volume 2 of the textbook on Tuesday.

Example 1 Determine if the triangles below are congruent. If the triangles are congruent, make a flowchart to justify your answer. A B D C

Example 2 > > A E C B D
Determine if the triangles below are congruent. If the triangles are congruent, make a flowchart to justify your answer. A E > C > B D

Conditions for Triangle Similarity
If you are testing for similarity, you can use the following conjectures: SSS~ All three corresponding side lengths have the same zoom factor AA~ Two pairs of corresponding angles have equal measures. SAS~ Two pairs of corresponding lengths have the same zoom factor and the angles between the sides have equal measure. NO CONJECTURE FOR ASS~ 14 6 7 3 10 5 55° 40° 40° 55° 40 20 70° 70° 30 15

Conditions for Triangle Congruence
If you are testing for congruence, you can use the following conjectures: SSS All three pairs of corresponding side lengths have equal length. ASA Two angles and the side between them are congruent to the corresponding angles and side lengths. SAS Two pairs of corresponding sides have equal lengths and the angles between the sides have equal measure. 5 3 7 7 3 5 10 55° 40° 40° 55° 10 20 20 70° 70° 15 15

Conditions for Triangle Congruence
If you are testing for congruence, you can use the following conjectures: AAS Two pairs of corresponding angles and one pair of corresponding sides that are not between them have equal measure. HL The hypotenuse and a leg of one right triangle have the same lengths as the hypotenuse and a leg of another right triangle. NO CONJECTURE FOR ASS 51 42° 51 42° 44° 44° 19 23 23 19

SAS SSS ASA AAS Problem 6-12 Complete 6-12 on page 295:
Use your triangle congruence conjectures to determine if the following pairs of triangles must be congruent. SAS SSS ASA AAS ASS SAS

SSS AAS ASS AAA Problem 6-12 Continued Complete 6-12 on page 295:
Use your triangle congruence conjectures to determine if the following pairs of triangles must be congruent. SSS AAS ASS AAA

Day 57: April 30th Homework Check and Correct (in red) & Warm-Ups!
Objective: Extend the use of flowcharts to document triangle congruence facts. Practice identifying pairs of congruent triangles and contrast congruence arguments with similarity arguments. THEN Recognize the converse relationship between conditional statements. Homework Check and Correct (in red) & Warm-Ups! Finish Problems 6-22 to 6-23 Problems 6-30 to 6-31 Chapter 6 Review Sheet Conclusion Homework: Problems 6-35 to 6-40 & BRING TEXTBOOK FROM HOME Ch. 6 Team Test TOMORROW & Ch. 6 Individual Test Friday Is your book damaged? Torn/missing pieces of book cover means that your book needs to be replaced. Bring $19 TOMORROW. If you think it can be repaired, see Ms. Katz – do NOT make a mess of it with tape! You will be getting Volume 2 of the textbook TOMORROW.

Warm-Up! April 30th

Practice with Congruent Triangles
Determine whether or not the two triangles in each pair are congruent. If they are congruent, show your reasoning in a flowchart. (1) (2) (3) A G 18 P 16 N 41° H D 22° 4 5 B C J K Q 18 5 41° 4 22° 16 L F R S M E

Day 58: May 1st Objective: Assess Chapter 6 in a team setting. THEN Review Chapters 5 and 6. Homework Check and Correct (in red) Chapter 6 Team Test Work on Chapter 6 Review Sheet Homework: Problems CL6-87 to 6-94 (and check solutions)

Level 2 Geometry Spring 2012 Ms. Katz.

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