1. Inequalities in Two Triangles
Section 5-6
Inequalities in Two Triangles

2. Hinge Theorem Comparing 2 triangles
Must have 2 pairs of corresponding congruent sides
Included angle of 1st > included angle of 2nd
Third side of 1st > Third side of 2nd

3. Example #1:
therefore… B A C
70° E D F
20°

4. Try it! 1. 2. 3.

5. Converse of the Hinge Theorem
Comparing 2 triangles
Must have 2 pairs of corresponding congruent sides
Third side of 1st > Third side of 2nd
Included angle of 1st > included angle of 2nd

6. Example: B A C
therefore… 15 E D F 4

7. Try It! 4. 5. 6.

8. Use an inequality to show the restriction on x based on the Hinge Theorem.
30°
35° 2x
3x-2
50°
35° 11 x
23°
45°
X+5
2x+4