1. 5-5 INEQUALITIES IN TRIANGLES Objectives: Students will be able to: 1) Use inequalities involving angles of triangles 2) Use inequalities involving sides of triangles

2. Think back…. What do we remember about the exterior angles of a triangle?

3. What is the largest angle shown?

4. Also remember that corollaries flow directly from theorems…

5. Why is m<4 is greater than m<5?

6. Try this….

7. Lets use sketchpad! Lets see if there is a relationship between angles and sides in triangles! Lets see if there is a relationship between angles and sides in triangles!

8. What did we see??? The largest angle was always opposite the largest side! The smallest angle is always opposite the smallest side!

9. Help Mr. Tessalone! Mr. Tessalone wants to build a bench in the largest corner of his triangular deck. Which angle should he build it in and why? What if he wants to put a plant in the smallest angle? Where would that go and why?

10. What if there is no diagram?

11. Think… Could we have a case where there is not one specific angle that is the largest? Come up with an example Be sure to label your angles with possible measurements correctly and use markings if needed. What type or types of triangles did you come up with?

12. What if we knew angle measures… Could we find the largest side? Could we find the smallest side? What do you think?

13. Converse to Theorem 5-10

14. List The Sides From Longest to Shortest! What is the measure of <Y? m<y = 80 What is the Largest Angle? The Smallest? XZ, XY, YZ

15. List the sides in order from shortest to longest.

16. Hungry? Lets have some pasta!

17. Your Challenge! Break your spaghetti into three pieces that will not form a triangle.

18. Compare the lengths… Compare the two combined lengths of the smaller pieces to the larger one. What do you see?

19. Triangle Inequality Theorem

20. Are Triangles Possible With these Lengths?

21. Got that?

22. What if I only know 2 Sides? What are all the possible lengths of the third side of a triangle if the other sides are 9 in and 17 in? Lets say the third side is the Largest Side. 9 + 17 > x 26 > x Lets say the third side is the Smallest Side. x + 9 > 17 x > 8

23. A Triangles sides are 3 in and 12 in. What could the third side be? Say x is a smaller side. Say x is the Largest Side