CCSS

G-CO 9: Prove theorems about lines and angles.

G-CO 10: Prove theorems about triangles.

G-CO 11: Prove theorems about parallelograms.

Lesson Goals Identify, name, and

describe polygons.

Unit 7 Lesson 2: Polygons

ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

Regular Interior Angle Corollary

180 2n

n

The measure of each interior angle of a regular polygon is

180( 2)n

n

Find the measure of one interior angle of a regular polygon with 15 sides.

example

180(15 2)

15

180(13)

15156

180( 2)165

n

n

The measure of each interior angle of a regular polygon is 165o.How many sides does the polygon have?

example

180 360 165n n

360 15n 24 n

Polygon Exterior Angle TheoremThe sum of the measures of the exterior angles of a convex polygon (one angle at each vertex) is 360o.

1

2

34

5

6

1 2 3 4m m m m 5 6 360m m

Knott’s Berry Farm

A portable ferris wheel in England

Austria - Vienna: Riesenrad - the Giant Wheel at the Prater

You Try

What is the sum of the measures of the interior angles of a decagon?

180 2n

180 10 2

180 8

1440

180 10 2

10

You Try

What is the measure of one interior angle of a regular decagon?

180 2n

n

1440

10

144

The measure of each interior angle of a regular polygon is 156o.How many sides does the polygon have?

example

Would it be possible for a regular polygon to have interior angles with the angle measure 130o?

example

No, a polygon cannot have 7.2 sides.

You Try

What is the sum of the measures of the exterior angles of a decagon?

360

You Try

What is the sum of the measures of the interior angles of a heptagon?

180 2n

180 7 2

180 5

900

180 7

7

2

You Try

What is the measure of one interior angle of a regular heptagon?

180 2n

n

900

7

900

You Try

What is the sum of the measures of the exterior angles of a heptagon?

360

You Try

What is the sum of the measures of the exterior angles of a polygon with 45 sides?

360

You Try

What is the sum of the measures of the exterior angles of a polygon with 27 sides?

360

Find the value of y.

example

2yo yo

2yoyo

2 2 360y y y y 6 360y

60y

Regular Polygon Exterior Angle Corollary

The measure of each exterior angles of a regular polygon

360

n

Find the value of x.

example

xo

360

n

360

6

60

The Regular Interior Angle Corollary extends the Polygon Regular Interior Angle Sum Theorem by __________________.

Polygon Exterior Angle Theorem shows that a polygon becomes closer to a _____ as the _____ of sides ______ because ________.

The Regular Polygon Exterior Angle Corollary extends the Polygon Exterior Angle Theorem by _____________.

Summary

Today’s Assignment #2

p. 665: 1, 5, 22 – 25, 29 – 37 o, 41, 51, 53