Question

Triangles A B C and T P Q are shown. Sides A C and T Q are congruent. Angles B C A and P Q T are congruent.

Which statements are true about additional information for proving that the triangles are congruent? Select two options.

If AngleA ≅ AngleT, then the triangles would be congruent by ASA.
If AngleB ≅ AngleP, then the triangles would be congruent by AAS.
If all the angles are acute, then the triangles would be congruent.
If AngleC and AngleQ are right angles, then triangles would be congruent.
If BC ≅ PQ, then the triangles would be congruent by ASA.

Answer 1

Correct choices: 1 and 2.

Why:
- If ∠A ≅ ∠T, then you have ∠A, AC, ∠C corresponding to ∠T, TQ, ∠Q — that is ASA, so the triangles are congruent.
- If ∠B ≅ ∠P, then you have two angles (∠B and ∠C) and a non‑included side AC corresponding to PQ and TQ — that is AAS, so the triangles are congruent.

Why the others are false:
- All angles being acute gives no congruence information.
- C and Q being right angles only gives both triangles are right; with only AC ≅ TQ (a leg) you still need a hypotenuse or another leg to apply HL or another congruence test.
- If BC ≅ PQ, then with AC ≅ TQ and ∠C ≅ ∠Q you actually get SAS (two sides and the included angle), not ASA — the conclusion (congruent) would be true but the stated reason ASA is incorrect.