PolygonsPolygons

Where has Polly gone?Where has Polly gone?

PolygonPolygon

A closed figure formed by joining three or A closed figure formed by joining three or more segments in a plane at their more segments in a plane at their endpoints, with each line segment joining endpoints, with each line segment joining exactly 2 others.exactly 2 others.

Each line segment is called a Each line segment is called a sideside of the of the polygon.polygon. This polygon

has 8 sides.

Circle the figures that are Circle the figures that are polygons:polygons:

Why are these NOT Why are these NOT polygons?polygons?

A. Open sideA. Open side

B. Curved sideB. Curved side C. Vertex has C. Vertex has

more than 2 more than 2 segments that segments that meetmeet

D. Curved sideD. Curved side

Vertex and diagonalVertex and diagonal

A A vertexvertex is where 2 sides meet. is where 2 sides meet. A A diagonaldiagonal joins two joins two

nonconsecutive vertices.nonconsecutive vertices. Name the vertices and the Name the vertices and the

diagonal in this polygon:diagonal in this polygon: Vertices: Vertices: A,B,C,D,E,FA,B,C,D,E,F Diagonal:Diagonal: CE CE

List all the diagonals in List all the diagonals in this polygon:this polygon:

DBDB DADA ECEC EBEB ACAC

Polygons are named by Polygons are named by the number of sides.the number of sides.

Name these polygons:Name these polygons:

A. triangleA. triangle B. QuadrilateralB. Quadrilateral C. PentagonC. Pentagon D. HexagonD. Hexagon E. OctagonE. Octagon F. DodecagonF. Dodecagon

Polygons with all sides and angles Polygons with all sides and angles equal are equal are regularregular polygons. Circle polygons. Circle the regular polygons:the regular polygons:

Polygons are named by Polygons are named by naming consecutive vertices naming consecutive vertices in order.in order.

Circle all the correct Circle all the correct names for this polygon:names for this polygon:

pentagon ABCDE

pentagon AEDCB

pentagon ACDBE

pentagon DCBAE

pentagon BDCAE

pentagon BAEDC

What is the sum of the What is the sum of the angle measures in a angle measures in a triangle?triangle?

Please draw a triangle on a piece of Please draw a triangle on a piece of scratch paper. It can be any size or scratch paper. It can be any size or shape, just be sure it is a triangle.shape, just be sure it is a triangle.

Now, tear off the three angles of the Now, tear off the three angles of the triangle. Position the angles side-by-side triangle. Position the angles side-by-side on your desk. What shape do they on your desk. What shape do they make?make?

Draw the angles side-by-side on your paper like this ↑

What is the measure of a What is the measure of a straight line?straight line?

The sum of the angles of The sum of the angles of any triangle is any triangle is 180°180°

Find the measure of Find the measure of the missing angle:the missing angle:

((3535 + +9090 - ) - )180180 = = 11ےے ((125125 - ) - )180180 = = 11ےے

5555 = = 11ےے °°

35°

90° 1ے

The sum of the angles of The sum of the angles of any triangle is any triangle is 180°180°

Find the measure of Find the measure of the missing angle:the missing angle:

((6565 + + 6565 - ) - )180180 = = 22ےے ((130130 - ) - )180180 = = 22ےے

5050 = = 22ےے °°

65°65°

2ے

Find x:Find x:

3x - 4 + 5x + 10 + 6x + 6 = 1803x - 4 + 5x + 10 + 6x + 6 = 180 14x + 12 = 18014x + 12 = 180 -12 -12-12 -12 14x = 16814x = 168

x = 12x = 12

What is the sum of the What is the sum of the angle measures in a angle measures in a polygon?polygon? We can divide the polygon We can divide the polygon into triangles, then multiply into triangles, then multiply the number of triangles by the number of triangles by 180180°°

How many triangles make up How many triangles make up this quadrilateral?this quadrilateral?

22 What is the sum of the angles What is the sum of the angles

of this quadrilateral?of this quadrilateral? 2 x 180° = 2 x 180° = 360°360°

What is the sum of the What is the sum of the angles in this hexagon?angles in this hexagon?

4 x 1804 x 180° = ° =

720°720°

What is the sum of the What is the sum of the angles in this pentagon?angles in this pentagon?

3 x 1803 x 180° = ° =

540°540°

Do you HAVE to draw the triangles Do you HAVE to draw the triangles to find out how many of them there to find out how many of them there are in a polygon?are in a polygon?

NO!NO!

4 sides, 5 sides, 6 sides,2 triangles 3 triangles 4 triangles

n sides, n-2 triangles!

What is the sum of the What is the sum of the measures of the angles of measures of the angles of these polygons?these polygons?

180(6-2) 180(8-2) 180(10-2)

= 180(4) =180(6) = 180(8)

= 720° = 1080° =1440°

Find the missing angle Find the missing angle measure in this polygon:measure in this polygon:

180)5-2(180)5-2( = 180)3(= 180)3( = 540= 540°°

540540° = 115 + 106 + 94 + 109 + X° = 115 + 106 + 94 + 109 + X 540 = 424 + X540 = 424 + X 116° = X116° = X

Find the missing angle Find the missing angle measure in this polygon:measure in this polygon:

180)9-2(180)9-2( = 180)7(= 180)7( = 1260= 1260°°

12601260° = 156 + 151 + ° = 156 + 151 + 138 + 156 + 140 + 138 + 156 + 140 + 130 + 133 + 135 +X130 + 133 + 135 +X

1260 = 1139 + X1260 = 1139 + X 121° = X121° = X