6.1 Polygons

Week 1 Day 2 January 7th 2014

Warm UP: Identifying Polygons

• State whether the figure is a polygon. If it is not, explain why.

F

E

D

CBA

Essential Question :

• What is a polygon? How do we identify and classify polygons? How do we find angle measures of quadrilaterals?

Vocabulary

• Polygon • Sides • Vertex of a polygon • Consecutive vertices• Diagonal of a polygon

Definitions• A polygon is a plane figure that is

formed by three or more segments called sides. (a closed, sided figure)

• Each side intersects exactly two other sides at each of its endpoints. Each endpoint is a vertex of the polygon.

• Two vertices that are endpoints of the same side are consecutive vertices.

• A segment that joins two nonconsecutive vertices of a polygon is called a diagonal.

Verticesside

diagonal

Consecutive vertices

Warm UP: Identifying Polygons

• State whether the figure is a polygon. If it is not, explain why.

• Not D – has a side that isn’t a segment – it’s an arc.

• Not E– because two of the sides intersect only one other side.

• Not F because some of its sides intersect more than two sides.

F

E

D

CBA

Figures A, B, and C are polygons.

Polygons are named by the number of sides they have. Fill in the blank.

Number of sides Type of polygon

3 Triangle

4

5

6

7

8

Quadrilateral

Pentagon

Hexagon

Heptagon

Octagon

Quadrilateral Interior Angles Theorem

• The sum of the measures of the interior angles of a quadrilateral is 360°.

A

B

C

D

m<A + m<B + m<C + m<D = 360°

Example

• Find m<Q and m<R.

R

x

P

S

2x°

Q

80°

70°

x + 2x + 70° + 80° = 360° 3x + 150 ° = 360 ° 3x = 210 ° x = 70 °

m< Q = xm< Q = 70 ° m<R = 2x

m<R = 2(70°)m<R = 140 °

Homework

• Page 306 # 8-10, 16, 18