Exercise 11 Page 637

How should we prove congruence?

From the diagram, we are given a pair of congruent corresponding sides and a pair of congruent corresponding angles in △ STR and △ QTP. With another congruent angle, we can show congruence of △ PTS and △ RTQ where ∠ 1 and ∠ 2 happen to be corresponding angles.

Plan for proving congruence

Our plan includes 3 steps.

1. Show that △ STR and △ QTP are congruent by the ASA Congruence Theorem.
2. Show that △ STP and △ QTR are congruent by the SAS Congruence Theorem.
3. Show that ∠ 1 and ∠ 2 are corresponding angles in △ STP and △ QTR.