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

Answers: 1 and 2.

Brief reasons:
- If ∠A ≅ ∠T then ∠A and ∠C with side AC between them give ASA → congruent.
- If ∠B ≅ ∠P then two angles (B,C) correspond to (P,Q) and AC ≅ TQ is the non‑included side → AAS → congruent.

The others are false:
- "All angles acute" doesn't force congruence.
- Right angles at C and Q plus AC ≅ TQ is only one leg, not enough (need HL or more).
- BC ≅ PQ would make the triangles congruent, but by SAS (two sides and included angle), not ASA.