1. 5.6: Inequalities in Two Triangles and Indirect Proof
GEOMETRY: Chapter 5
5.6: Inequalities in Two Triangles and Indirect Proof

2. Theorem 5.14: Hinge Theorem
If two sides of one triangle are congruent to two
sides of another triangle, and the included angle
of the first is larger
than the included angle
of the second, then the
third side of the first is
longer than the third
side of the second.
Image taken from: Geometry. McDougal Littell: Boston, P. 335.

3. Theorem 5.15: Converse of the Hinge Theorem
If two sides of one triangle are congruent to two
sides of another triangle, and the third side of
the first is longer than
the third side of the
second, then the
included angle of the
first is larger than the
included angle of the second.
Image taken from: Geometry. McDougal Littell: Boston, P. 335.

4. Ex.1
Image taken from: Geometry. McDougal Littell: Boston, P. 336.

5. Ex.2
Two runners start together and run in opposite directions. Each one goes 1.5 miles, changes directions, and goes 2.4 miles. The first runner starts due north and turns 100 degrees towards the east. The other runner starts dues south and turns 130 degrees towards the west. Both runners return to the starting point. Which runner ran farther? Explain.
Image taken from: Geometry. McDougal Littell: Boston, P. 337.

6. 5.6, p. 305, #7-14 all