Question

The isosceles triangle theorem says \"if two sides of a triangle are congruent, then the angles opposite those sides are congruent\". . . If you are using this figure to prove the isosceles triangle theorem, what would be the best strategy?

Answer 1

The correct answer for this question is letter C, because then you know that PS = SR, QS = QS (of course) and PQ=QR (given), then triangles are congruent and thus angle QPS equals angle QRS and the triangle PQR is then isosceles

Answer 2

The correct answer is:

C) Draw QS so that S is the midpoint of PR, then prove ΔPQS is congruent to ΔRQS using SSS.

Explanation:

We cannot use ∠P or ∠R in the proof, since they are part of the theorem we are trying to prove.

We know that PQ and QR are congruent, as we are given that information. If we draw a segment from Q to PR, this segment will be part of both triangle PQS and RQS. This gives us 2 sides congruent.

If we draw QS so that S is the midpoint of PR, then by definition PS is congruent to SR. This gives us 3 sides of both triangles that are congruent, which means the side-side-side congruence theorem applies and the triangles are congruent.

Since the triangles are congruent, this means corresponding angles are congruent, and ∠P is congruent to ∠R.