# Polygons Where has Polly gone?.

## Presentation on theme: "Polygons Where has Polly gone?."— Presentation transcript:

Polygons Where has Polly gone?

Polygon A closed figure formed by joining three or more segments in a plane at their endpoints, with each line segment joining exactly 2 others. Each line segment is called a side of the polygon. This polygon has 8 sides.

Circle the figures that are polygons:

Why are these NOT polygons?
A. Open side B. Curved side C. Vertex has more than 2 segments that meet D. Curved side B C D

Vertex and diagonal A vertex is where 2 sides meet.
A diagonal joins two nonconsecutive vertices. Name the vertices and the diagonal in this polygon: Vertices: A,B,C,D,E,F Diagonal: CE

List all the diagonals in this polygon:
DB DA EC EB AC E B C D

Polygons are named by the number of sides.

Name these polygons: A E B C F D A. triangle B. Quadrilateral
C. Pentagon D. Hexagon E. Octagon F. Dodecagon E B C F D

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

Polygons are named by naming consecutive vertices in order.
Circle all the correct names for this polygon: pentagon ABCDE pentagon AEDCB pentagon ACDBE pentagon DCBAE pentagon BDCAE pentagon BAEDC

What is the sum of the angle measures in a triangle?
Please draw a triangle on a piece of scratch paper. It can be any size or shape, just be sure it is a triangle.

Now, tear off the three angles of the triangle
Now, tear off the three angles of the triangle. Position the angles side-by-side on your desk. What shape do they make? a straight line! Draw the angles side-by-side on your paper like this ↑

What is the measure of a straight line?
180

The sum of the angles of any triangle is 180°
Find the measure of the missing angle: ے1 = (90 +35) ے1 = (125) ے1 = 55° 35° 90° ے1

The sum of the angles of any triangle is 180°
Find the measure of the missing angle: ے2 = ( ) ے2 = (130) ے2 = 50° ے2 65° 65°

Find x: 3x - 4 + 5x + 10 + 6x + 6 = 180 14x + 12 = 180 -12 -12
14x = 168 x = 12

What is the sum of the angle measures in a polygon?
We can divide the polygon into triangles, then multiply the number of triangles by 180° How many triangles make up this quadrilateral? 2 What is the sum of the angles of this quadrilateral? 2 x 180° = 360°

What is the sum of the angles in this hexagon?
720°

What is the sum of the angles in this pentagon?
3 x 180° = 540°

Do you HAVE to draw the triangles to find out how many of them there are in a polygon?
NO! 4 sides, 5 sides, sides, 2 triangles triangles triangles n sides, n-2 triangles!

What is the sum of the measures of the angles of these polygons?
180(6-2) 180(8-2) 180(10-2) = 180(4) =180(6) = 180(8) = 720° = 1080° =1440°

Find the missing angle measure in this polygon:
180(5-2) = 180(3) = 540° 540° = X 540 = X 116° = X

Find the missing angle measure in this polygon:
180(9-2) = 180(7) = 1260° 1260° = X 1260 = X 121° = X