Geometry

• Agenda

1. ENTRANCE

2. Go over Practice

3. Quiz

4. 3-4 The Polygon Angle-Sum Theorems

5. Practice Assignment

6. EXIT

Practice

• Quiz Time

Good Luck!!!

Chapter 3

3-4 The Polygon Angle-Sum Theorems

Polygon

• A _______ figure that consists of three or more segments joined at the endpoints and each segment must meet exactly two other segments.

Polygon Terms

• 3 sides Triangle• 4 sides Quadrilateral• 5 sides Pentagon• 6 sides Hexagon• 7 sides Heptagon• 8 sides Octagon• 9 sides Nonagon• 10 sides Decagon• 11 sides Undecagon• 12 sides Dodecagon• n sides n-gon

Naming A Polygon

• A polygon is named by the number of _______.

ex: If a polygon has

___ sides, you use

___ letters.

Polygon ABCDE

Types of Polygons

• Convex– The diagonals are entirely inside the figure.

• Concave– At least one diagonal is partly outside the

figure.

Regular Polygon

• Remember: equilateral, equiangular

• A regular polygon is a polygon that is both equilateral and equiangular.

Theorem 3-9Polygon Angle-Sum Theorem

• The sum of the measures of the angles of an n-gon is (n-2)180.

ex: This pentagon

has 5 sides.Sum = (n-2)180

Sum = (5-2)180

Sum = (3)180

Sum = 540

Theorem 3-10Polygon Exterior Angle-Sum

Theorem

• The sum of the measures of the ________ angles of a polygon, one at each vertex, is 360.

ex: This pentagon has 5 sides.

The sum of the 5exterior angles is360.

Example #1

• Name the ________. Identify vertices, sides, and angles. Is it concave or convex?

Example #2

• Find the interior angle sum.

a. 13-gon b. decagon

Example #3

• How many sides does each polygon have if its interior angle sum is:

a. 2700 b. 1080

Example #4

• Find x.

Example #5

• Find y.

Example #6

• Find x.

Example #7

• Find x.

Example #8

• Find x.

Example #9

• How many sides does each regular polygon have if its exterior angle is:

a. 120 b. 24

Example #10

• How many sides does each regular polygon have if its interior angle is:

a. 90 b. 144

• Practice– WB 3-4 # 1-19

• EXIT