Day 51: November 16th Objective: Create regular polygons with a hinged mirror, and use reflection and congruence to learn more about the central angle of these shapes. Also, learn more about the diagonals of rhombi. THEN Introduce proof, and learn more properties of parallelograms and kites. HW Check/Correct in RED AND… Do PAGE 3 in Congruence Packet INDEPENDENTLY – hand-in! Take Notes in LL on Math Notes – Page 346 Define/Take Notes on “Reflexive Property” HINT: Use glossary! Problems 7-36 to 7-38 Two Proof Examples to lead into the next section Homework: Problems 7-6 to 7-10 AND 7-14 to 7-18

Day 52: November 17th Objective: Introduce proof, and learn more properties of parallelograms and kites. HW Check/Correct in RED AND… Do PAGE 4 in Congruence Packet INDEPENDENTLY – hand-in! LL Notes: Key Observations from yesterday’s mirror activity Lesson 7.2.1 (Properties & Proofs about parallelograms and kites) Homework: Problems 7-26 to 7-35 [Double set – leave time!]

Day 53: November 20th Objective: Introduce proof, and learn more properties of rhombi and squares. HW Check/Correct in RED AND… Complete flowchart proofs for two statements on the board Properties & Proofs about rhombi and squares Homework: Problems 7-39 to 7-43 AND 7-49 to 7-53 (Skip 51)

Day 54: November 21st Objective: Introduce proof, and learn more properties of rectangles and trapezoids. HW Check/Correct in RED AND… Complete flowchart proofs for two statements on the board Properties & Proofs about rectangles and trapezoids Homework: Problems 7-58 to 7-62 AND 7-66 to 7-70 AND Properties of Quadrilaterals WS

Day 56: November 27th Objective: Introduce the format of a two-column proof. THEN Continue to develop proof-writing skills as new properties of triangles and quadrilaterals are proven. HW Check/Correct in RED AND… Mark each diagram from the board appropriately, given the directions Problems 7-78 to 7-79 Problem 7-88 Toolkit Addition: Triangle Midsegment Theorem Look at common theme in Problems 7-29, 60, 69 Introduce Section 7.3 (Problem 7-98) Homework: Problems 7-72 to 7-76 AND 7-83 to 7-87 Chapter 6-7 Team Test Thursday Chapter 6-7 Individual Test Next Mon or Tues

Theorem Toolkit

Day 57: November 28th Objective: Investigate quadrilaterals for special properties, such as parallel sides or a right angle. Also, review many algebraic tools and apply these skills to analyze shapes on a coordinate grid. THEN Develop methods for finding the midpoint of a segment on a coordinate grid as the study of coordinate geometry is continued. HW Check/Correct in RED AND… LAST proof in the “Proof Skeletons” packet you’re getting right now Problems 7-99 to 7-101 Problems 7-107 to 7-111 Homework: Problems 7-94 to 7-96 AND 7-102 to 7-106 Chapter 6-7 Team Test Thursday Chapter 6-7 Individual Test Next Monday

Day 58: November 29th Objective: Review concepts from Chapters 6-7. HW Check/Correct in RED Problems 7-109 to 7-110 Proof Practice WS #7-10 Chapter 7 Review Worksheet Homework: Problems 7-113 to 7-116 Chapter 6-7 Individual Test Monday

Day 59: November 30th Objective: Assess Chapters 6-7 in a team setting. HW Check/Correct in RED Review yesterday’s work Chapter 6-7 Team Test Homework: Problems 7-119 to 7-123 Chapter 6-7 Individual Test Monday

Day 60: December 1st Objective: Assess Chapters 6-7 in a team setting. HW Check/Correct in RED Review Chapter 6-7 Team Test Go over the Chapter 7 Review Sheet Introduce Chapter 8 Problems 8-12 to 8-15 Homework: Problems 7-124 to 7-132 AND STUDY!!! Chapter 6-7 Individual Test Monday

Day 61: December 4th Objective: Assess Chapters 1-7 in an individual setting. THEN Learn how to find the sum of the interior angles of a polygon and apply this skill to solve problems. Silence your cell phone and put it in your assigned pocket in the back of the room Get a ruler, pencil/eraser, and calculator out First: Take the test Second: Check your work Third: Hand the test & formula sheet to Mrs. Poppiti when finished Fourth: Check last night’s homework Homework: Finish Problems 8-13 to 8-15 & DO 8-6 to 8-11

Day 62: December 5th Objective: Learn how to determine the measure of an interior and exterior angle of a regular polygon. THEN Consolidate our understanding of finding the number of sides and angles of a regular polygon. HW Check/Correct in RED Review Problems 8-13 to 8-15 Problems 8-22 to 8-26 Problems 8-33 to 8-35 Homework: Problems 8-16 to 8-21 AND 8-27 to 8-32

Polygon Interior Angle Sum 180° 180° 180° 180° 180° 180° # of Sides 3 4 5 6 7 8 9 10 12 Interior Angle Sum 180° 360° 540°

Polygon Interior Angle Sum 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° # of Sides 3 4 5 6 7 8 9 10 12 Interior Angle Sum 180° 360° 540° 720° 900° 1080°

Polygon Interior Angle Sum 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° 180° # of Sides 3 4 5 6 7 8 9 10 12 Interior Angle Sum 180° 360° 540° 720° 900° 1080° 1260° 1440° 1800°

Interior Angle Sum of n-gons If a polygon has n sides, the interior angle sum is: 180°( n - 2 )

Interior Angle of an n-gon If a regular polygon has n sides, the measure of one interior angle is: 180°( n - 2 ) n

Exterior Angle Sum of an n-gon The sum of the exterior angles of any polygon is 360º. If a regular polygon has n sides, the measure of one exterior angle is: 360° ÷ n

Day 63: December 6th Objective: Develop an algorithm to find the area of any regular polygon. THEN Learn about the ratio of the areas of similar figures. HW Check/Correct in RED AND Finish Problem 8-35 Problems 8-43 to 8-48 Start Problems 8-61 to 8-64? Homework: Problems 8-37 to 8-42 AND 8-49 to 8-54

Day 64: December 7th Objective: Learn about the ratio of the areas of similar figures. THEN Continue to develop an understanding for how the area and perimeter of a shape change as the shape is enlarged or reduced proportionally. HW Check/Correct in RED Problems 8-61 to 8-64 Problems 8-71 to 8-75 Homework: Problems 8-55 to 8-60 AND 8-65 to 8-70 Chapter 8 Team Test Monday (?) Chapter 8 Individual Test Wed or Thurs (?)

Ratio of the areas of similar figures is… Ratios of Similarity Linear Scale Factor: 1 Linear Scale Factor: 2 Linear Scale Factor: 3 Linear Scale Factor: 4 Ratio of Area to 1st : 1 Ratio of Area to 1st : 4 Ratio of Area to 1st : 9 Ratio of the areas of similar figures is the square of the linear scale factor Ratio of the areas of similar figures is… Ratio of Area to 1st : 16

Day 65: December 8th Objective: Discover the area and circumference formulas for a circle. THEN Use the ratios of areas of similar figures to develop a method of finding the area and circumference of a circle with any sized radius. Also, develop methods to find the area of sectors and the length of arcs. HW Check/Correct in RED AND Complete problems left on your table Finish Problems 8-73, 8-74 Problems 8-82 to 8-83 Problems 8-91 to 8-93 LL Entry: Area and Circumference Extra Practice WS: Area and Circumference Homework: Problems 8-76 to 8-81 AND 8-85 to 8-90 Chapter 8 Team Test Wednesday (?) Chapter 8 Individual Test Thurs or Fri (?)

Polygons with Infinite Sides # of sides 3 4 5 6 8 9 ≈Area 1.30 2.00 ≈Perimeter 5.20 5.66 # of sides 3 4 5 6 8 9 ≈Area ≈Perimeter # of sides 10 15 30 60 90 180 ≈Area ≈Perimeter # of sides 10 15 30 60 90 180 ≈Area 3.05 3.12 3.14 ≈Perimeter 6.24 6.27 6.28 23

Circumference (Perimeter) of Circle Area/Circumference: Problem 8-91 Radius Length Area of Circle Circumference (Perimeter) of Circle 1 π un2 3 4 5 7 10 r 2π units 9π un2 6π units 16π un2 8π units 25π un2 10π units 49π un2 14π units 100π un2 20π units πr2 un2 2πr units 24

Circumference of a Circle (Perimeter) Circle Formulas Diameter of a Circle Circumference of a Circle (Perimeter) Area of a Circle Circle X or X d r C X

Day 66: December 11th Objective: Use the ratios of areas of similar figures to develop a method of finding the area and circumference of a circle with any sized radius. Also, develop methods to find the area of sectors and the length of arcs. THEN Use problem-solving strategies to find areas of circular and polygonal regions in context. HW Check/Correct in RED AND Do Area/Circ. WS – Show All Work! Problem 8-94 LL Entry: Arc Length and Sector Area Extra Practice WS: Arc Length and Sector Area Problems 8-102 to 8-104 if time Homework: Problems 8-96 to 8-101 AND 8-106 to 8-111 Chapter 8 Team Test Tomorrow Chapter 8 Individual Test Thurs or Fri (?)

Arc Length A measure of a portion of the circumference of a circle. OR

Area of a Sector The area of the region bounded by two radii of the circle and their intercepted arc. or

Example 1 C 3 cm 90° A B Circle C

Example 2 In a circle, an arc whose angle is 10° has a length of 25π cm. Find the radius of the circle.

Example 3 Find the area of the shaded region. 120° 5 cm