Question

Which additional information could be used to prove that the triangles are congruent using AAS or ASA? Check all that apply.

Answer 1

Answer: it’s A,B, and D

Answer 2

Consider the given triangles.

Given:
`\angle C \cong \angle Q`

ASA congruence criterion states that if two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

AAS congruence criterion states that if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Consider the first part:

1. In triangles ABC and QPT

If we take
`\angle B \cong \angle P , BC \cong PQ` along with the given condition.

Then the triangles are congruent by ASA congruence criterion.

2. If we take
`\angle A \cong \angle T` and
`AC= TQ=3.2` along with the given condition.

Then the triangles are congruent by ASA congruence criterion.

3. As,
`\angle C \cong \angle Q`,
`\angle A \cong \angle T` and
`\angle B \cong \angle P`, so the triangles can not be congruent.

4. If we take
`\angle A \cong \angle T` and
`BC \cong PQ` along with the given condition.

Then the triangles are congruent by AAS congruence criterion.

5. If we take AC=TQ=3.2 and CB=QP=3.2 along with the given condition, then the triangles are congruent but by SAS congruence criteria neither by ASA nor AAS congruence criterion.