Answer:
Triangle PST ≅ Triangle PQR by ASA
Step-by-step explanation:
We know that because line segments PS and PR are congruent, then ∠PRS and ∠PSR must also be congruent because of the Isosceles Triangle Theorem, which states that if two sides of a triangle are congruent, then angles opposite those sides are congruent.
Therefore, the angles supplementary to ∠PRS and ∠PSR (∠PRQ and ∠PST respectively) must also be congruent to each other since we've already stated that ∠PRS and ∠PSR are congruent due to the Isosceles Triangle Theorem.
So, we can prove triangles PST and PQR congruent by ASA (Angle-Side-Angle).
