If Angle A ≅ Angle T, then the triangles would be congruent by ASA
If Angle B ≅ Angle P, then the triangles would be congruent by AAS.
We are told that;
Sides AC and TQ are congruent.
Angles BCA and PQT are congruent.
Thus, we can say that;
Side AC and side TQ are congruent.
Angle BCA and angle PQT are congruent too.
Since angle A and angle T are congruent, it means the congruency theorem used will be ASA(Angle - Side - Angle) Theorem.
Lastly, if angle B were to be congruent to angle P, it means the congruency theorem used will be AAS(Angle - Angle - Side) Theorem.
The missing options are;
A) If AngleA ≅ AngleT, then the triangles would be congruent by ASA.
B) If AngleB ≅ AngleP, then the triangles would be congruent by AAS.
C) If all the angles are acute, then the triangles would be congruent.
D) If AngleC and AngleQ are right angles, then triangles would be congruent.
E) If BC ≅ PQ, then the triangles would be congruent by ASA.
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