November 17, 2017

number of sides

Name of polygon

3

4

5

6

7

8

10

n

triangle

quadrilateral

pentagon

hexagon

heptagon

octagon

decagon

n-gon

Warmup:

Complete the table by naming each polygon.

November 17, 2017

Do not need to know just fun to know...

November 17, 2017

Geometry Section 5.1

Polygons &

their angle measures

Learning Target:I can calculate angle measure for angles of polygons. [G.MG.1]

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polygon NOT a polygon

Polygon - a ________ plane figure with 3 or more __________ sides

and each vertex connects only ___________.

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A polygon is convex if no line that contains a side of the polygon passes through the interior of the polygon.

A polygon that is not convex is called concave.

How can you remember concave?

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polygon not a polygon convex concave

Tell whether the figure is a polygon and whether it is convex or concave.

a. b.

c. d.

(name the logo)

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A polygon is

all interior angles ≅

all sides ≅ AND all int angles ≅

all sides ≅equilateral -

equiangular -

regular -

Equilateral EquiangularRegular

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equilateral regular

Classify the polygon by the number of sides. Tell whether the polygon is equilateral, equiangular or regular. Explain your reasoning.

a. b.

c.

equiangular

d.

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Activity: Exploring the Sum of the Interior and Exterior Angles of convex polygons

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POLYGON INTERIOR ANGLES THEOREMThe sum of the measures of the interior angles of a convex polygon with n sides is

POLYGON EXTERIOR ANGLES THEOREMThe sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is ________.

m∠1 + m∠2 + m∠3 + m∠4 + m∠5 = 360

http://www.mathsisfun.com/geometry/exterior-angles-polygons.html

SUM Interior ∠s = (n – ___ ) _______

SUM Exterior ∠s = ______

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2) The sum of the interior angles of a polygon is 1980˚, classify the polygon by the number of sides.

1) Find the sum of the interior angles of

a) decagon b) 15-gon

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xo

(x + 20)˚

112˚96o

4) Find the value of x.

3) Find the value of x.Hint: find the sum of the interior angles first

Hint: find the sum of the exterior angles first

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5) Find the measure of one interior ∠ AND one exterior ∠ on a stop sign.

6) Each interior angle of the regular n-gon has a measure is 162˚. Find the value of n.

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Homework:5.1 Angles in Polygons

Sum Interior = (n – 2) • 180

Sum Exterior = 360˚

In a Regular Polygon

Each Interior =n

(n – 2) •180

Each Exterior = n 360

Assignment: 5.1 worksheet

November 17, 2017