Polygons Where has Polly gone?.

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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 = 180 - (90 +35) ے1 = 180 - (125) ے1 = 55° 35° 90° ے1

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

Find x: 3x - 4 + 5x + 10 + 6x + 6 = 180 14x + 12 = 180 -12 -12 -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, 6 sides, 2 triangles 3 triangles 4 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° = 115 + 106 + 94 + 109 + X 540 = 424 + X 116° = X

Find the missing angle measure in this polygon: 180(9-2) = 180(7) = 1260° 1260° = 156 + 151 + 138 + 156 + 140 + 130 + 133 + 135 +X 1260 = 1139 + X 121° = X

raise your achievement practice will raise your achievement The End