SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle...

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SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review HW (20 min) 3. New notes / exit slip (5 – 15 min) Warm-Up: 1. What is 80% of 90% of 10? 2. What is 20% of 15% of 100? 3. What is 25% of 70% of 150? (round to nearest tenth) HW: Read Pgs 353-355 Do Pg. 356 #1-#3 Quiz Thursday! Mon, 2/3

Transcript of SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle...

Page 1: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min)2. Review HW (20 min)3. New notes / exit slip (5 – 15 min)

Warm-Up:

1. What is 80% of 90% of 10?

2. What is 20% of 15% of 100?

3. What is 25% of 70% of 150?

(round to nearest tenth)HW: Read Pgs 353-355

Do Pg. 356 #1-#3Quiz Thursday!

Mon, 2/3

Page 2: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

The sum of the interior measures of the angles of a triangle is 180 degrees.

Triangle Sum Theorem

Page 3: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

The measures of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

Triangle Exterior Angle Theorem

Page 4: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.
Page 5: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

Review HW:Page 175: #1 – #21 ALL

Page 177: #29 – #32 ALL

Page 6: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

Exit Slip: ½ sheet – Collected1.) Find the value of x, y, and z?

3.) Find m<1 and m<2.2.) Find the value of x

Page 7: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

Summary

Be VERY specific!1. Sum of interior angles of a triangle = 1800

2. Exterior angle = Sum of interior angles in triangle

Page 8: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

SWBAT… find the sum of the measures of interior and exterior angles of a polygon. Agenda 1. Warm-up / HW Check (10 min)2. New notes / practice problems (40 min)

Warm-Up:

1. What is 40% of 5/2?

2. What is 65% of ¾?

3. What is 80% of 7/12?

Pg. 356 #1 – #3, Pg. 356 #7 – #25 ALLQuiz Thursday!

Tues, 2/4

Page 9: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

Chapter 6.1 Polygon Angle – Sum

Page 10: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

Polygon

A closed plane figure formed by 3 or more segments that all lie in one plane

Page 11: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

Polygons are named by number of sidesNumber of Sides Polygon

34

5

6

78

9

10

12

n

TriangleQuadrilateral

Pentagon

Hexagon

Heptagon

Octagon

Nonagon

Decagon

Dodecagon

n-gon

Page 12: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

An equilateral polygon: All sides congruent. An equiangular polygon: All angles congruent. A regular polygon: All the sides and angles

congruent.

Equilateral Polygon Equiangular Polygon Regular Polygon

Page 13: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

Concave

If any part of a diagonal contains points in the exterior of the polygon.

Page 14: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

Convex If no diagonal contains points in the exterior.

A regular polygon is always convex.

Page 15: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

SWBAT… find the sum of the measures of interior and exterior angles of a polygon. Agenda 1. Warm-up (10 min)2. Notes / practice problems (40 min)

Warm-Up:1. Al is paid 35% as much as Franklin. If Franklin is

paid $24.00 per hour, how much is Al paid per hour?

2. Nancy gets paid $12.00 per hour at her job at the grocery store. Susie is paid 120% as much as Nancy. How much is Susie paid per hour?

Pg. 356 #1 – #3, Pg. 356 #7 – #25 ALLQuiz Tomorrow!

Wed, 2/5

Page 16: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

Polygon # of sides(n)

# of triangles Sum of interior angles of a polygon

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Octagon

n-gon

3

4

5

6

7

8

n

3

4

5

6

n – 2

2

1 180°

2 · 180 = 360°

3 · 180 = 540°

4 · 180 = 720°

5 · 180 = 900°

6 · 180 = 1080°

(n – 2) · 180°

Page 17: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

Ex: What is the measure of angle Y in pentagon TODAY?

(5 2) 180m T m O m D m A m Y

110 90 120 150 3 180m Y 470 540m Y

70m Y

Page 18: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

SWBAT… find the sum of the measures of interior and exterior angles of a polygon. Agenda 1. Warm-up (10 min)2. Notes / practice problems (40 min)

Warm-Up:1. Tomas bought a new book on sale. It cost $17.95

but was on sale for 20% off. How much did the book cost Tomas?

2. Roman bought a shirt for $11.25. He was able to receive a discount on the shirt for 30% off. How much did Roman pay for the shirt?

Pg. 421 #5 – 10

Fri, 2/6

Page 19: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

Polygon Angle-Sum Theorem

The sum of the measures of the interior angles of an n-gon is: Sum = (n – 2)180

n = the number of sides

Page 20: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

Ex: What is the sum of the measures of the interior angles of an octagon?

Sum = (n – 2)180

= (8 – 2)180

= 6 * 180

= 1,080°

Page 21: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

1. Ex: If the sum of the measures of the interior angles of a convex polygon is 3600°, how many sides does the polygon have.

(n – 2)180 = 3600180n – 360 = 3600 + 360 + 360 180n = 3960 180 180 n = 22 sides

(n – 2)180 = Sum

Page 22: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

1. Ex: If the sum of the measures of the interior angles of a convex polygon is 2340°, how many sides does the polygon have.

(n – 2)180 = 2340180n – 360 = 2340 + 360 + 360 180n = 2,700 180 180 n = 15 sides

(n – 2)180 = Sum

Page 23: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

4x – 2

82

108

2x + 10108 + 82 + 4x – 2 + 2x + 10 = (4 – 2)180

6x + 198 = 3606x = 162 6 6

x = 27

Ex: Solve for x

Sum = (n – 2)180

Page 24: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

Ex. Find the values of the variables and the measures of the angles.

x = 251300

900

1150

1150

900

Page 25: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

The measure of each interior angle of a regular n-gon is ( 2) 180

.n

n

Page 26: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

Ex: What is the measure of each or one interior angle in a regular octagon?

( 2) 180.

n

n

(8 – 2)180 / 8

1350

Page 27: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

What do you notice about the exterior angles of the polygons below?

Page 28: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

Polygon Exterior Angle-Sum Theorem

The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.

1 2 3 4 5 360m m m m m

Page 29: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

Ex. Find the exterior angle sum of a decagon.

Page 30: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

54⁰

68⁰

65⁰

(3x + 13)⁰

60⁰

(4x – 12)⁰

Sum of exterior angles is 360°

(4x – 12) + 60+ (3x + 13) + 65 + 54+ 68 = 360 7x + 248 = 360 – 248 – 248 7x = 112 7 7 x = 12

Ex: Find the value of x

Page 31: SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

Ex: What is the measure of angle 1 in the regular octagon?

3601

8m

1 45m


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