Question

In the given figure PS = PR, Angle TPS = Angle QPR. prove that Triangle PST = Triangle PQR

Answer 1

Triangle PST ≅ Triangle PQR by ASA

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).