warmup

A

B

C2x

3x

4x-20

Find the measureof the exterior angle at C

Ch. 10.1: Polygons

p. 514-521

M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios (sine, cosine, tangent) within mathematics or across disciplines or contexts (e.g., Pythagorean Theorem, Triangle Inequality Theorem).

GSE’s

Primary

Polygon: remember your work with quadrilaterals. Think of this definition.

Regular Polygon: all angles and sides of the polygon are congruent (always convex)

List the specific names for a regular 3 sided and 4 sided polygon.

Convex polygon: if you extend any side of the polygon, you will not go through the figure

Concave polygon: the opposite is true (it caves in)

A B

C

D

EF

G

H

1) Pick any vertice.2) Make a darker point at it.3) Connect that point to every other vertice in the polygon

Write down how many non-overlapping triangles are formed.

Exterior angle

Extend any one side of the figure

x

y

Reminder from ch. 4

HANDOUT on investigating polygons angles

•The formula for finding the sum of the interior angles of any convex polygon is :

•The sum of all exterior angles of any convex polygon is:

The formula for finding one interior angle in any regular polygon.

Kite ABRN

2x

80 Find the measure of angle N

2x110

50

130115

80

Solve for x in the Hexagon

The measure of one of the interior angles

of a regular polygon is 160. How many

sides does the regular polygon have?

Homework