1. Explain why solving proportions is an important skill for solving geometry problems. Give an example problem that you would use proportions to solve.

2. Explain why all isosceles right triangles are similar, but not all scalene right triangles are similar. Choose one a theorem, postulate, or corollary in the chapter to help with your explanation

3. How is the Triangle-Angle-Bisector Theorem similar to Corollary 2 of Theorem 7-3? How is it different?

4. In triangle FGH, the bisector of angle F also bisects the opposite side. The ratio of each half of the bisected side to each of the other sides is 1 : 2. What type of triangle is triangle FGH? Explain.

5. An angle bisector of a triangle divides the opposite side of the triangle into segments 3 in. and 6 in long. A second side of the triangle is 5 in long. Find the length of the third side of the triangle. Explain how you arrived at the correct length.