Unit 7 Unit 7 Lesson 1 Polygons CCSS

Unit 7

Unit 7 Lesson 1: Polygons CCSS Lesson Goals Prove theorems about ¥ Identify, name, and lines and angles. describe polygons. G-CO 10: Prove theorems about triangles. G-CO 11: Prove theorems about parallelograms. G-CO 9: ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

Previously in Math: Polygon 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

Previously in Math: Polygon C D A B E F L K H G J I polygon ABCDEFGIJKL

Previously in Math: Polygon Not a Polygon

Previously in Math: Classification triangle 3 hexagon 6 quadrilateral 4 heptagon 7 octagon 8 pentagon 5

Previously in Math: Classification 9 12 nonagon dodecagon n 10 decagon n-gon

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

Classification Convex All vertices “point” outward.

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

Classification Concave At least one vertex “points” inward.

You Try Classify by number of sides. octagon

You Try Convex or Concave? concave

You Try Classify by number of sides. dodecagon

You Try Convex or Concave? convex

You Try Classify by number of sides. heptagon

You Try Convex or Concave? concave

Previously in Math: Classification Equilateral: all sides congruent Equiangular: all angles congruent Regular: equilateral and equiangular

Polygon Interior Angles Theorem The sum of the measures of the interior angles of a convex polygon is where n is the number of sides. 1 2 3 4

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

example Find x.

example Find x.

example Find the value of x.

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

Summary A polygon is _________. A polygon is classified by _________, or ____. A regular polygon has _______. The Polygon Interior Angle Sum Theorem says ______.

Today’s Assignment p. 325: 2 – 9, 21 – 23, 27 -30, 38, 42 – 46 e p. 665: 8, 12, 14, 16

Assignment Check p. 325: 2 – 9, 21 – 23, 27 -30, 38, 42 – 46 e ü p. 665: 8, 12, 14, 16 ü

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.

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

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

Unit 7 Lesson 1 b: Polygons CCSS Lesson Goals Prove theorems about ¥ Identify, name, and lines and angles. describe polygons. G-CO 10: Prove theorems about triangles. G-CO 11: Prove theorems about parallelograms. G-CO 9: ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

Regular Interior Angle Corollary The measure of each interior angle of a regular polygon is

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

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

Polygon Exterior Angle Theorem The sum of the measures of the exterior angles of a convex polygon (one angle at each vertex) is 360 o. 6 1 5 2 4 3

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?

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

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

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

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

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

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

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

example Find the value of y. yo 2 yo y o 2 yo

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

example Find the value of x. xo

Summary 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 _______.

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

Check Assignment ü p. 325: 47 – 51 ü 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. 22. 144 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. 32. 15 24 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. 34. 20 o 18

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