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Polygons

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.

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Polygons

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  1. Polygons Where has Polly gone?

  2. 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.

  3. Circle the figures that are polygons:

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

  5. 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

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

  7. Polygons are named by the number of sides.

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

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

  10. 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

  11. 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.

  12. 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 ↑

  13. What is the measure of a straight line? 180

  14. 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

  15. 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°

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

  17. 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°

  18. What is the sum of the angles in this hexagon? • 4 x 180° = • 720°

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

  20. 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 triangles3 triangles4 triangles n sides, n-2 triangles!

  21. 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°

  22. 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

  23. 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

  24. practice will raise your achievement The End

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