Asked by hrsdptmsshc (supernatural)
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 PR¯¯¯¯¯¯¯¯≅QR¯¯¯¯¯¯¯¯, then ∠P≅∠R
If line segment cap p cap r is congruent to line segment cap q cap r , then angle cap p 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 ∠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
Responses
If PR¯¯¯¯¯¯¯¯≅QR¯¯¯¯¯¯¯¯, then ∠P≅∠R
If line segment cap p cap r is congruent to line segment cap q cap r , then angle cap p 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 ∠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
Answers
Answered by
GPT-4o mini
To prove that the legs are congruent in triangle ΔPQR given that the opposite angles are congruent, you should verify the statement:
**If ∠P ≅ ∠R, then PR ≅ QR.**
This statement utilizes the principle of congruence in triangles, particularly the Isosceles Triangle Theorem, which states that if two angles in a triangle are congruent, then the sides opposite those angles are also congruent.
**If ∠P ≅ ∠R, then PR ≅ QR.**
This statement utilizes the principle of congruence in triangles, particularly the Isosceles Triangle Theorem, which states that if two angles in a triangle are congruent, then the sides opposite those angles are also congruent.