Honors Geometry Spring 2012 Ms. Katz.

Honors 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 1-15 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 LL – “Graphing an Equation” Problems 1-47 to 1-53 Problems 1-59 to 1-62 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)

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

Day 3: February 1st 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) LL – “Rigid Transformations” Problems 1-68 to 1-72 Problems 1-87 to 1-91 LL – “Slope-Intercept Form” and “Parallel and Perpendicular Lines” Conclusion Homework: Problems 1-73 to 1-77 AND 1-82 to 1-86; GET SUPPLIES; Extra credit tissues or hand sanitizer

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 15 15

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. 16

Day 4: February 2nd Objective: Learn how to classify shapes by their attributes using Venn diagrams. Also, review geometric vocabulary and concepts, such as number of sides, number of angles, sides of same length, right angle, equilateral, perimeter, edge, and parallel. THEN Continue to study the attributes of shapes as vocabulary is formalized. Become familiar with how to mark diagrams to help communicate attributes of shapes. Homework Check and Correct (in red) Finish Problems 1-89 to 1-91 LL – Several entries Problems 1-97 to 1-98 Problems to 1-108 Conclusion Homework: Problems 1-92 to 1-96 AND 1-99 to 1-103; Get 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) 18

1-72 B A A’ 19 19

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 20 20

Reflection across a Side
The two shapes MUST meet at a side that has the same length. 21 21

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 necessary! 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

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 5: February 3rd Objective: Continue to study the attributes of shapes as vocabulary is formalized. Become familiar with how to mark diagrams to help communicate attributes of shapes. THEN Develop an intuitive understanding of probability, and apply simple probability using the shapes in the Shape Bucket. Homework Check and Correct (in red) Wrap-Up Problems to 1-108 Problems to 1-119 Closure Problems CL1-126 to [Choose problems you need to work on as individuals] Conclusion Homework: Problems to AND to 1-125; Supplies! Chapter 1 Team Test Monday

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?

Shape Bucket 38

Day 6: February 6th Objective: Assess Chapter 1 in a team setting. 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) Chapter 1 Team Test (≤ 45 minutes) Start Problems 2-1 to 2-7 Conclusion Homework: Problems 2-8 to 2-12 Chapter 1 Individual Test Friday

2-2 A C’ C B B’

Day 7: February 7th Objective: 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. THEN 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. Homework Check and Correct (in red) Finish Problems 2-1 to 2-7 Problems 2-13 to 2-17 Start Problems 2-23 to 2-28 Conclusion Homework: Problems 2-18 to 2-22 AND 2-29 to 2-33 Chapter 1 Individual Test – Is Thursday okay instead?

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°

Marcos’ Tile Pattern How can you create a tile pattern with a single parallelogram? 44 44

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. 45 45

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. 46 46

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. 47 47

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. 48 48

Why Parallel Lines? 53° x 49 49

2-16 X X

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)

Day 8: February 8th 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. Also, apply knowledge of angle relationships to analyze the hinged mirror trick from Lesson Homework Check and Correct (in red) Review Chapter 1 Team Test & Algebra Review Finish Problems 2-26 to 2-28 Problems 2-43 to 2-50 Conclusion Homework: Problems 2-38 to 2-42 and STUDY (or do the next set of HW) Chapter 1 Individual Test is TOMORROW

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

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° > >

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

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 57

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 9: February 9th 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 Fifth: Work on 2-46/47/48 with your x-value Homework: Problems 2-51 to 2-55 AND 2-61 to 2-65 Optional EC: Problem 2-49 neatly done and well- explained on separate paper to hand-in Monday

Day 10: February 10th Objective: 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 Wrap-Up Problems 2-46 to 2-50 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 Check PowerSchool Sunday night to see if your test grade has been posted! 

Warm Up! February 10th 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

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
66

Obtuse Triangle Height Extra Base
Area of Obtuse Triangle = Area of Right Triangle = ½ (Base)(Height) 67

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

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 72

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 75

Day 11: February 13th Objective: Explore how to find the height of a triangle given that one side has been specified as the base. Also, find the areas of composite shapes using what has been learned about the areas of triangles, parallelograms, and trapezoids. THEN Review the meaning of square root. Recognize how a square can help find the length of a hypotenuse of a right triangle. Homework Check and Correct (in red) Do Problem 2-79 while you wait for Ms. Katz Review Chapter 1 Individual Test Problems 2-86 to 2-89 Problems 2-95 to 2-99 Estimating Square Roots and Simplifying Radicals Lesson Homework: Problems 2-90 to 2-94 and to 2-104 Optional EC: Problem 2-80 (Separate paper, neat, etc) – Wed. Team Test Wednesday; Individual Friday (?)

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

Note card = Height Locator
Base “Weight”

Day 12: February 14th Objective: Review the meaning of square root. 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. THEN Develop and prove the Pythagorean Theorem. Homework Check and Correct (in red) Finish Problems 2-95 to 2-99 Estimating Square Roots and Simplifying Radicals Lesson Problems 2-105, to 2-108 Start Problems to 2-117 Homework: Problems to and to 2-122 Optional EC: Problem 2-80 (Separate paper, neat, etc) – Wed. Team Test Tomorrow; Individual Tues/Wed (?)

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 13: February 15th Objective: Develop and prove the Pythagorean Theorem. THEN Assess Chapter 2 in a team setting. Homework Check and Correct (in red) Finish Problems to 2-117 Chapter 2 Team Test Homework: Problems CL2-123 to CL2-131 Chapter 2 Individual Wednesday

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

Day 14: February 16th ***NEW SEATS***
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. THEN 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. ***NEW SEATS*** Homework Check and Correct (in red) & Warm-Up! Problems 3-2 to 3-5 Problems 3-10 to 3-15 Homework: Problems 3-6 to 3-9 AND 3-17 to 3-21 Chapter 2 Individual Wednesday

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

Enlarging

Exactly same shape but not necessarily same size
Similar Figures Exactly same shape but not necessarily same size 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

Day 15: February 17th 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) & Warm-Up! Problems 3-22 to 3-25 Problems 3-32 to 3-37 Conclusion Homework: Problems 3-27 to 3-31 AND 3-38 to 3-42 Chapter 2 Individual Wednesday

Warm Up! February 17th If Rob has three straws of different lengths: 4 cm, 9 cm, and 6 cm. Will he be able to make a triangular picture frame out of the straws? Why or why not? Find the area of the following shapes: 20 ft 7 ft 30.7 ft 16.3 ft 28 ft 4.2 ft 3 ft 10 ft 40 ft 10 ft

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

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 ~ 96 96

Writing a Proportion 25 s 13 10 AB ABCD ~ WXYZ BC WX XY AB AB WX WX =
97 97

Day 16: February 21st Objective: Learn the SSS~ and AA~ conjectures for determining triangle similarity. THEN Review Chapter 1 and 2 topics. Homework Check and Correct (in red) & Warm-Up! Finish Problem 3-36 Problems 3-43 to 3-47 Review Ch. 2 Team Test (and comments) Time? Review Ch. 1 and 2 Topics Conclusion Homework: Problems 3-48 to 3-52 AND STUDY! Chapter 2 Individual Test Tomorrow!

Warm Up! February 21st Solve the following equations for x: 1. 2.

Day 17: February 22nd 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: Give test & formula sheet to Ms. Katz when you’re done Fourth: Correct last night’s homework Homework: Problems 3-59 to 3-63 [We’ll be finishing Ch. 3 this week…tests coming again soon! ]

Day 18: February 23rd Objective: Learn how to use flowcharts to organize arguments for triangle similarity, and continue to practice applying the AA~ and SSS~ conjectures. THEN 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. Homework Check and Correct (in red) Problems 3-53 to 3-58 Problems 3-64 to 3-67 Problem 3-73 Conclusion Homework: Problems 3-68 to 3-72

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 corresponding angles have equal measure, then the triangles are similar.

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 19: February 24th 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 our reasoning in a flowchart. Homework Check and Correct (in red) Problems 3-73 to 3-77 Problems 3-83 to 3-86 Conclusion Homework: Problems 3-78 to 3-82 AND 3-88 to 3-92 [Optional E.C. – Problem 3-87 neatly and well-done for Monday] Chapter 3 Team Test Monday Chapter 3 Individual Test Wednesday

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 20: February 27th Objective: Apply knowledge of similar triangles to multiple contexts. THEN Assess Chapter 3 in a team setting. Homework Check and Correct (in red) & Collect Optional Problem 3-87 Review Chapter 2 Individual Test Problems 3-93 to 3-95 Chapter 3 Team Test Conclusion Homework: Problems 3-96 to and CL3-101 to CL3-110 Chapter 3 Individual Test Wednesday

Day 21: February 28th Objective: Apply knowledge of similar triangles to multiple contexts. THEN Review Chapters 1-3 for tomorrow’s individual test. Homework Check and Correct (in red) Problems 3-93 to 3-95 Review Chapters 1-3 Conclusion Homework: Problems 4-6 to 4-10 Chapter 3 Individual Test Tomorrow

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 60 110

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 123 111

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. 163 112

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

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

Day 22: February 29th 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: Give test & formula sheet to Ms. Katz when you’re done Fourth: Correct last night’s homework Homework: Relax! ½ day tomorrow [and feel extremely fortunate that for ONE night this semester, you do not have math homework]

Day 23: March 1st Objective: Recognize that all the 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. No HW Check! Problems 4-1 to 4-5 Conclusion Homework: Problems 4-11 to 4-14 [Note: These are classwork problems]

Day 24: March 5th 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. 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. Learn how to find the slope ratio using a scientific calculator. Homework Check and Correct (in red) Review Problems 4-11 to 4-14 Do Problem 4-15 Problems 4-21 to 4-24 Start Problems 4-30 to 4-35 Conclusion Homework: Problems 4-16 to 4-20 AND 4-25 to 4-29

Day 25: March 6th 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. Learn how to find the slope ratio using a scientific calculator. THEN Apply knowledge of tangent ratios to find measurements about the classroom. Homework Check and Correct (in red) Warm-Up Review Problems Problems 4-30 to 4-35 Problems 4-41 to 4-42 Review Chapter 3 Individual Test Conclusion Homework: Problems 4-36 to 4-40 AND 4-43 to 4-47 Chapter 4 Team Test Friday

Warm-Up! March 6th The area of the triangle below
is 42 in2. Calculate DC. 8 in. 10 in. D B A C

Warm-Up! March 6th Solve for x: hypotenuse x 68° 25 cm

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 26: March 7th Objective: Apply knowledge of tangent ratios to find measurements about the classroom. THEN Learn how to list outcomes systematically and organize outcomes in a tree diagram. THEN Continue to use tree diagrams and also introduce a table to analyze probability problems. Also, investigate the difference between theoretical and experimental probability. Homework Check and Correct (in red) Talk about Tomorrow’s Math Contest (last of the year) Problem 4-42 Problems 4-48 to 4-53 Problems 4-59 to 4-62 Conclusion Homework: Problems 4-54 to 4-58 AND 4-63 to 4-67 Chapter 4 Team Test Friday

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 127

Day 27: March 8th Objective: Continue to use tree diagrams and also introduce a table to analyze probability problems. Also, investigate the difference between theoretical and experimental probability. THEN Learn how to use an area model to represent a situation of chance. THEN Develop more complex tree diagrams to model biased probability situations. Further consider the difference between theoretical and experimental probability. Homework Check and Correct (in red) Finish Problems 4-60 to 4-62 Problems 4-68 to 4-70 Problems 4-77 to 4-80 Conclusion Homework: Problems 4-72 to 4-76 AND 4-82 to 4-86 Chapter 4 Team Test Tomorrow Problem 4-71 is optional extra credit (Get handout from Ms. Katz)

4-60: Tree Diagram $100 $300 $1500 START Keep $100 Double $200 Keep
$600 $1500 Keep $1500 Double $3000 129

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

Day 28: March 9th Objective: Assess Chapter 4 in a team setting. THEN Learn about the sine and cosine ratios. Also, start a Triangle Toolkit. Homework Check and Correct (in red) Chapter 4 Team Test Problem 4-80 (One more tree diagram to practice) Start Problems 5-1 to 5-6 Conclusion Homework: Problems 4-91 to 4-95 AND CL4-96 to CL4-105 Problem 4-71 is optional extra credit (Get handout from Ms. Katz) Due Monday Chapter 4 Individual Test Friday

Day 29: March 12th Objective: Learn about the sine and cosine ratios. Also, start a Triangle Toolkit. Homework Check and Correct (in red) & Collect 4-71 (E.C.) Finish Problems 5-1 to 5-6 Review Chapter 4 Team Test Conclusion Homework: Problems 5-7 to 5-11 Chapter 4 Individual Test Friday

Day 30: March 13th Objective: 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) & Sign up for Pi Day Snacks Review Chapter 4 Team Test Problem 4-80 on Index Card – hand one in as a team for grade Finish Problem 5-6 Start Problems 5-12 to 5-15 Conclusion Homework: Problems 5-16 to 5-20 Bring circular food for tomorrow that you signed up for Chapter 4 Individual Test Friday

Day 31: March 14th Objective: 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) Problems 5-12 to 5-15 & Eat Snacks Clean Up – “Everybody, do your share!” Conclusion Homework: Problems 5-26 to 5-30 Chapter 4 Individual Test Friday

Trigonometry SohCahToa h o a

Day 32: March 15th Objective: Understand how to use trigonometric ratios to find the unknown angle measures of a right triangle. Also, introduce the concept of “inverse.” THEN Review for Chapter 4 Individual Test. THEN Use sine, cosine, and tangent ratios to solve real world application problems. Homework Check and Correct (in red) Problems 5-21 to 5-25 Ask/Answer any questions from Chapters 1-4 If time, start Problems 5-31 to 5-35 Conclusion Homework: Problems 5-36 to 5-40 AND Study like it’s your job! Chapter 4 Individual Test Tomorrow

Day 33: March 16th 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 5-33 to 5-35 [Note: These are classwork problems]

Day 34: March 19th 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. Also, practice recognizing and applying all three of the new triangle shortcuts. Homework Check and Correct (in red) Review Problems 5-33 to 5-35 Problems 5-41 to 5-45 Problems 5-51 to 5-55 Conclusion Homework: Problems 5-46 to 5-50 AND 5-56 to 5-60

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 35: March 20th Objective: Learn to recognize 3:4:5 and 5:12:13 triangles, and find other examples of Pythagorean triples. Also, 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

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 36: March 21st Objective: 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. THEN 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. THEN Complete the Triangle Toolkit by developing the Law of Cosines. Homework Check and Correct (in red) Finish Problems 5-61 to 5-65 Problems 5-73 to 5-76 Start Problems 5-85 to 5-88 Conclusion Homework: Problems 5-79 to 5-84 AND 5-89 to 5-94 Ch. 5 Team Test Soon?

Day 37: March 22nd Objective: Review and practice using the Law of Sines. THEN Complete the Triangle Toolkit by developing the Law of Cosines. Homework Check and Correct (in red) Summarize Law of Sines in Angle Toolkit Practice WS - #1,2,6,7 on Law of Sines Problems 5-85 to 5-88 Practice Law of Cosines if time Conclusion Homework: Problems to 5-105 Ch. 5 Team Test Tomorrow Midterm (Ch. 5 Individual Test) Next Friday

Day 38: March 23rd Objective: Complete the Triangle Toolkit by developing the Law of Cosines. THEN Assess Chapter 5 in a team setting. Homework Check and Correct (in red) Practice Law of Sines and Cosines Chapter 5 Team Test Problem 5-95 and Discussion Conclusion Homework: Problems to Double set! Midterm (Ch. 5 Individual Test) Next Friday

Day 39: March 26th Objective: Learn that multiple triangles are sometimes possible when two side lengths and an angle not between them are given (SSA). THEN Apply current triangle tools to solve multiple problems and applications. Homework Check and Correct (in red) Problem 5-95 and Discussion Problems to 5-113 Review Chapter 5 Team Test Conclusion Homework: Problems CL5-126 to CL5-136 Midterm (Ch. 5 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 exam.]

Day 40: March 27th Objective: Practice identifying congruent triangles by first determining that the triangles are similar and that the ratio of corresponding sides is 1. THEN Use our understanding of similarity and congruence to develop triangle congruence shortcuts. Homework Check and Correct (in red) Problems 6-1 to 6-3 Problems 6-10 to 6-12 Conclusion Homework: Problems 6-4 to 6-9 AND 6-13 to 6-18 Midterm (Ch. 5 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 exam.]

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

Day 41: March 28th 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, and then investigate the relationship between the truth of a statement and the truth of its converse. Homework Check and Correct (in red) Finish Problem 6-12 Problems 6-19 to 6-23 Problems 6-30 to 6-33 Homework: Problems 6-24 to 6-29 AND 6-35 to 6-40 Chapter 6 Team Quiz Tomorrow (?) Midterm (Ch. 5 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 exam.]

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

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

Day 42: March 29th Objective: Assess Chapter 6 in a team setting. THEN Review Chapters 1-5 as needed. Homework Check and Correct (in red) Chapter 6 Team Quiz Review/Ask Questions for Midterm Homework: Problems 6-43 to 6-48 Midterm (Ch. 5 Individual Test) Tomorrow!

Day 43: March 30th Objective: Assess Chapters 1-5 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 exam & formula sheet to Ms. Katz when you’re done Fourth: Correct last night’s homework Homework: Problems 6-61 to 6-66 Bring your Geometry textbook from home on Tuesday!!! Enjoy your week away from school!

*Beginning of Quarter 4*
Day 44: April 10th Objective: Review recent assessments. THEN Review for Chapter 6 individual test. *Beginning of Quarter 4* Homework Check and Correct (in red) Trade Textbooks Review Midterm (With example slides and OSCAR data) Review Chapter 6 Team Quiz Do Chapter 6 Closure Homework: Problems 7- Chapter 6 Individual Test Friday

Honors Geometry Spring 2012 Ms. Katz.

Similar presentations

Presentation on theme: "Honors Geometry Spring 2012 Ms. Katz."— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

Honors Geometry Spring 2012 Ms. Katz.

Similar presentations

Presentation on theme: "Honors Geometry Spring 2012 Ms. Katz."— Presentation transcript:

Similar presentations

About project

Feedback