Question

For ΔPQR , which statement should you verify in order to prove that the legs are congruent if the opposite angles are congruent?(1 point) Responses If ∠Q≅∠R , then PR¯¯¯¯¯¯¯¯≅PQ¯¯¯¯¯¯¯¯ If angle cap q is congruent to angle cap r , then line segment cap p cap r is congruent to line segment cap p cap q If PR¯¯¯¯¯¯¯¯≅PQ¯¯¯¯¯¯¯¯ , then ∠Q≅∠R If line segment cap p cap r is congruent to line segment cap p cap q , then angle cap q is congruent to angle cap r If ∠P≅∠R , then PR¯¯¯¯¯¯¯¯≅QR¯¯¯¯¯¯¯¯ If angle cap p is congruent to angle cap r , then line segment cap p cap r is congruent to line segment cap q cap r If PR¯¯¯¯¯¯¯¯≅QR¯¯¯¯¯¯¯¯ , then ∠P≅∠R

Answer 1

To prove that the legs (PR and PQ) are congruent given that the opposite angles (∠Q and ∠R) are congruent in triangle ΔPQR, you can use the following statement:

**If ∠Q ≅ ∠R, then PR ≅ PQ.**

This conclusion stems from the fact that in a triangle, if two angles are congruent, then the sides opposite those angles are also congruent. This is a direct application of the Angle-Side-Angle (ASA) theorem or the Side-Angle-Side (SAS) theorem depending on which angles and sides you are comparing.

So the correct response is:

**If ∠Q ≅ ∠R, then PR ≅ PQ.**