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  1 2 3 ALWAYS!!!

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

10. Quadrilateral Draw a diagonal…what do you get? Two triangles 1 23 4 5 6

11. Quadrilateral Each triangle = 180  Therefore the two triangles together = 360  1 23 4 5 6 180 

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 

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? Number of sides Number of triangles Angle sum of polygon 31 180  42 360  53 6 7 8

19. Find the nth term Number of sides Number of triangles Angle sum of polygon 31 180  42 360  53 6 7 8 9 10 nthn

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

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

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

23. Quadrilateral 100  +80  +55  +125  = 360  100  125  80  55  80  55  100  125 

24. Pentagon 72  * 5 = 360  108  72 

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  135  Calculate by: Angle Sum Number of sides