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Triangle Sum Theorem

Triangle Sum Theorem. Draw a Triangle. Make sure your lines are dark!. Tear off two vertices…. Line up the 3 angles (all vertices touching). What do they make?. A straight line = 180°. Angle sum of a Triangle. 180 ° <1 + <2 + <3 = 180 °. 2. ALWAYS!!!. 1. 3. Consider a Quadrilateral.

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Triangle Sum Theorem

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  1. Triangle Sum Theorem

  2. Draw a Triangle

  3. Make sure your lines are dark!

  4. Tear off two vertices….

  5. Line up the 3 angles (all vertices touching)

  6. What do they make?

  7. A straight line = 180°

  8. Angle sum of a Triangle • 180° • <1 + <2 + <3 = 180° 2 ALWAYS!!! 1 3

  9. Consider a Quadrilateral • What is the angle sum? <1 + <2 + <3 + <4 = ?

  10. Quadrilateral • Draw a diagonal…what do you get? 2 3 5 1 4 Two triangles 6

  11. Quadrilateral • Each triangle = 180° 2 3 5 180° 180° 1 4 Therefore the two triangles together = 360° 6

  12. Angle sum of a Quadrilateral • 180° + 180° = 360°

  13. Consider a Pentagon • What is the angle sum?

  14. Pentagon • Draw the diagonals from 1 vertex How many triangles?

  15. Angle sum of a Pentagon • Draw the diagonals from 1 vertex 180° 180° 180°

  16. Continue this process through Decagon • Draw the diagonals from 1 vertex

  17. Continue this process through Decagon • Draw the diagonals from 1 vertex

  18. What about a 52-gon? • What is the angle sum? Sorry I can’t draw it. • Can you find the pattern?

  19. Find the nth term

  20. Exterior angle sum • Now that you can find the angle sum of a polygon, what about the exterior angle sum? 35° 80° 65°

  21. Exterior angle sum • Note: Extend each side of the triangle. This makes a LINEAR PAIR 145° 35° 115° 100° 80° 65°

  22. Exterior angle sum • Add up the exterior angles • 100°+145°+115°= • 360° 145° 35° 115° 100° 80° 65°

  23. Quadrilateral • 100°+80°+55°+125° = 360° 125° 100° 80° 55° 55° 100° 125° 80°

  24. Pentagon 72° • 72° * 5 = 360° 108° 72° 108° 108° 72° 72° 72° 108° 108°

  25. What conclusion can you come up with regarding the exterior angle sum of a CONVEX polygon??

  26. The exterior angle sum of a CONVEX polygon = 360°

  27. Interior Angle Measure of a REGULAR polygons 60° 90° Equilateral Triangle Angle measure = 60° Square Angle measure = 90° These are measurement that we generally know at this time, But what about the other regular polygons? How do we calculate the interior angle measure?

  28. Interior Angle Measure of a REGULAR polygons 72° 120° Calculate by: Angle Sum Number of sides 135°

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