Polygons 1

Polygons 1 - Transcript

A polygon is a plane figure that is formed by three or more segments called sides Each side intersects exactly two other sides at each of its endpoints Each endpoint is a vertex of the polygon Two vertices that are the endpoints of the same side are called consecutive vertices Ex In polygon PQRST R and S are consecutive vertices A segment that joins two nonconsecutive vertices of a polygon is called a diagonal Ex Polygon PQRST has two diagonals from vertex R RP and RT
Q Q R R Vertex Side Vertex P Diagonals T S

6 1 Polygons 1 14 08

P

T

S

Is the figure a polygon Explain your reasoning a b

Identify Polygons

Yes The figure is a polygon Formed by four straight sides

No The figure is not a polygon because it has a side that is not a segment

Is the figure a polygon Explain your reasoning c d

Identify Polygons Cont

No The figure is not a polygon because two of the sides intersect only one other side

Yes The figure is a polygon formed by six straight sides

Classifying Polygons
Types of Polygons Triangle 3 sides Quadrilateral 4 sides Pentagon 5 sides Hexagon 6 sides Heptagon 7 sides Octagon 8 sides

Decide whether the figure is a polygon If so tell what type If not explain why a b

Classify Polygons

The figure is a polygon with four sides so it is a quadrilateral

The figure is not a polygon because it has some sides that are not segments

Decide whether the figure is a polygon If so tell what type If not explain why c d

Classify Polygons Cont

The figure is a polygon with five sides so it is a pentagon

The figure is not a polygon because some of the sides intersect more than two other sides

The sum of the measures of the interior angles of a quadrilateral is 360 m 1 m 2 m 3 m 4 360
2

Quadrilateral Interior Angles Theorem

1

3

4

Find Angle Measures of Quadrilaterals
Find the measure of Q
80

S

70 R P 70

Use the fact that the sum of the measures of the interior angles of a quadrilateral is 360 m P m Q m R m S 360 70 80 70 m S 360 220 m S 360 m S 140 So the measure of S is 140

S

More Practice
Textbook p 306 307 3 10 15 20 Homework Worksheet 6 1