1. Objective
Apply inequalities in two triangles.

3. Example 1A: Using the Hinge Theorem and Its Converse
Compare mBAC and mDAC.

4. Example 1B: Using the Hinge Theorem and Its Converse
Compare EF and FG.

5. Example 1C: Using the Hinge Theorem and Its Converse
Find the range of values for k.

6. Example 2: Travel Application
John and Luke leave school at the same time. John rides his bike 3 blocks west and then 4 blocks north. Luke rides 4 blocks east and then 3 blocks at a bearing of N 10º E. Who is farther from school? Explain.

7. Example 3a: Proving Triangle Relationships
Write a two-column proof.
Given:
Prove: AD > CB
Proof:

8. Check It Out! Example 3b
Write a two-column proof.
Given: C is the midpoint of BD.
m1 = m2
m3 > m4
Prove: AB > ED

9. Check It Out! Example 3c
Write a two-column proof.
Given:
SRT  STR
TU > RU
Prove: mTSU > mRSU