1.5: Polygons

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1.5: Polygons. =convex and concave. p. 514-521. GSE’s. Primary.

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## 1.5: Polygons

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1.5: Polygons

=convex and concave

p. 514-521

GSE’s

Primary

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).

Polygon: a closed figure with straight sides

http://en.wikipedia.org/wiki/File:Assorted_polygons.svg

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)

Triangle Sum
• The sum of the measures of the interior angles of a triangle is 180o.
• mA + mB+ mC=180o

+ + = 180

A

B

C

Example 1
• Name Triangle AWE by its angles

mA + mW+ mE=180o

(3x+5) + ( 8x+22) + (4x-12) = 180

A

15x + 15 = 180

15x = 165

x = 11

3x +5

mA = 3(11) +5 = 38o

8x + 22

mW = 8(11)+22 = 110o

4x - 12

W

mE = 4(11)-12 = 32o

E

Triangle AWE is obtuse

A

B

C

H

G

D

F

E

1) Pick any vertex.

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

x

y

Extend any one side of the figure

The angle formed is the

exterior angle. It’s a linear pair

With the inside angle

Springboard p. 93

HANDOUT on investigating polygons angles

Convex Polygon Number of Number of Sum of interior Sum of ext.

sides ‘s Angles 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:
Regular Polygons
• Polygons where each angle and side is congruent

What is an example of a regular 4 sided polygon?

How about a 3 sided polygons?

Kite ABRN

80

Find the measure of angle N

120

120

The measure of one of the interior angles

of a regular polygon is 160. How many

sides does the regular polygon have?