Question

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

Explanation:

Step1: Check Congruence for Pair A

For pair A, we look at the triangles. There is no information (like side - side - side (SSS), side - angle - side (SAS), etc.) that can confirm the congruence of the two triangles.

Step2: Check Congruence for Pair B

For pair B, we have right - angled triangles. The two legs (marked with one and two ticks respectively) and the right - angle (included angle) are equal. By the SAS (Side - Angle - Side) congruence criterion, the two right - angled triangles are congruent.

Step3: Check Congruence for Pair C

For pair C, we have two angles (marked) equal. By the AA (Angle - Angle) similarity, but since the triangles are of the same type (let's assume they are isosceles as the base angles are equal and the non - base angles are equal), and if we consider the side between the two angles (ASA - Angle - Side - Angle, if we assume the sides between the equal angles are equal in length as the triangles are drawn in a congruent - looking way), the two triangles are congruent.

Answer:

B and C only