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. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

a 2-dimensional plane figure Formed by three or more line segments Adjacent sides are non-collinear Each side intersects exactly 2 other sides at their endpoints

A B C D E I H F G J L K polygon ABCDEFGIJKL

triangle quadrilateral pentagon hexagon heptagon octagon

nonagon decagon dodecagon n-gon

Convex No line that contains a side passes through the interior of the polygon interior

Convex All vertices “point” outward.

Convex No line that contains a side passes through the interior of the polygon Concave A polygon that is not convex interior

Concave At least one vertex “points” inward.

Classify by number of sides. octagon

Convex or Concave? concave

Classify by number of sides. dodecagon

Convex or Concave? convex

Classify by number of sides. heptagon

Convex or Concave? concave

Equilateral: all sides congruent Equiangular: all angles congruent Regular: equilateral and equiangular

The sum of the measures of the interior angles of a convex polygon is where n is the number of sides

Find the sum of the measures of the interior angles of a convex decagon.

Find x.

Find the value of x.

Find the measure of each interior angle. Is the quadrilateral regular? D B C A Not regular

A polygon is __________________. A polygon is classified by _________, _________, or ________. A regular polygon has _____________. The Polygon Interior Angle Sum Theorem says ____________.

p. 325: 2 – 9, 21 – 23, , 38, 42 – 46 e p. 665: 8, 12, 14, 16

p. 325: 2 – 9, 21 – 23, , 38, 42 – 46 e p. 665: 8, 12, 14, 16

CONVEX OR CONCAVE Use the number of sides to tell what kind of polygon the shape is. Then state whether the polygon is convex or concave.

RECOGNIZING PROPERTIES State whether the polygon is best described as equilateral, equiangular, regular, or none of these.

TRAFFIC SIGNS Use the number of sides of the traffic sign to tell what kind of polygon it is. Is it equilateral, equiangular, regular, or none of these?

ANGLE MEASURES Use the information in the diagram to find.

USING ALGEBRA Use the information in the diagram to solve for x.

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. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

The measure of each interior angle of a regular polygon is

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

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

The sum of the measures of the exterior angles of a convex polygon (one angle at each vertex) is 360 o

Knott’s Berry Farm A portable ferris wheel in England

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

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

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

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

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

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

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

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

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

Find the value of y. 2yo2yo yoyo 2yo2yo yoyo

The measure of each exterior angles of a regular polygon

Find the value of x. xoxo

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 _____________.

p. 325: 47 – 51 p. 665: 18 – 24 e, 30 – 36 e, 55, 56

p. 325: 47 – 51 p. 665: 18 – 24 e, 30 – 36 e, 55, 56

ANGLE MEASURES In Exercises 14–19, find the value of x.

DETERMINING NUMBER OF SIDES In Exercises 22–25, you are given the measure of each interior angle of a regular n-gon. Find the value of n o 10

DETERMINING ANGLE MEASURES In Exercises 29–32, you are given the number of sides of a regular polygon. Find the measure of each exterior angle o

DETERMINING NUMBER OF SIDES In Exercises 33–36, you are given the measure of each exterior angle of a regular n-gon. Find the value of n o 18

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