Question

which of the following pairs show(s) two congruent triangles? a and b only b and c only a, b, and c c only

Explanation:

Step1: Recall congruence criteria

Two triangles are congruent if they have the same shape and size. Criteria include SSS (side - side - side), SAS (side - angle - side), ASA (angle - side - angle), AAS (angle - angle - side) and HL (hypotenuse - leg for right - triangles).

Step2: Analyze pair A

In pair A, the triangles have different sizes, so they are not congruent.

Step3: Analyze pair B

In pair B, the triangles have the same angles but no information about side - lengths being equal. Just having equal angles makes them similar, not congruent.

Step4: Analyze pair C

In pair C, we can see that two sides and the included angle are marked as equal. By the SAS (side - angle - side) congruence criterion, these two triangles are congruent.

Answer:

D. C only