1. 4.7 Triangle Inequalities

2. Relationship between SIDES and ANGLES:
In every triangle, the longest side is opposite the largest angle.
In every triangle, the shortest side is opposite the smallest angle.

3. Example 1:
Name the angles from largest to smallest:

4. Example 2:
Name the sides from longest to shortest:

5. You Try It…

6. A Few More…

7. Can ANY 3 segment lengths make a triangle?

8. Triangle Inequality Theorem
The SUM of the lengths of ANY 2 SIDES of a triangle is GREATER THAN the length of the third side.

9. Example 3:
Can the side lengths form a triangle? Explain.

10. Can the side lengths form a triangle? Explain.

11. Can the side lengths form a triangle? Explain.

12. You Try It…