Chapter 5 Review
Problem 15 proof
Because PQRS is a parallelogram, QR ∥ PS. Thus, since they are vertical angles, ∠APS ≅ ∠QAP. We are given that PA bisects ∠QPS, so ∠APQ ≅ ∠APS. By transitivity, ∠APQ ≅ ∠QAP. Using an angle-side theorem, this means that PQ ≅ QA. Since A is the midpoint of QR, QA ≅ AR, so by transitivity, PQ ≅ AR. Since PQRS is a parallelogram, QP ≅ RS. Another application of transitivity shows that AR ≅ RS. Then we can use that same angle-side theorem to show that ∠RAS ≅ ∠RSA. Because they are alternate interior angles between parallel lines, ∠RAS ≅ ∠ASP. By yet another transitivity, ∠RSA ≅ ∠ASP, which by defition means that ray SA bisects ∠RSP.
- 5.7 problem 15
- 5.7 problem 20