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 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
Regular Polygon Exterior Angle Corollary
The measure of each exterior angles of a regular polygon
360
n
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
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