Question

which pair of triangles is congruent by angle - angle - side? 1 2 3 4

Explanation:

Step1: Analyze Pair 1

In pair 1, we have vertical angles (equal), and two sides marked equal. But this is \(ASA\) (Angle - Side - Angle) congruence, not \(AAS\).

Step2: Analyze Pair 2

In pair 2, we have two angles (marked with arcs) and a non - included side (marked with two dashes) equal. This satisfies the \(AAS\) (Angle - Angle - Side) congruence criterion.

Step3: Analyze Pair 3

In pair 3, we have a right angle, a side (marked with one dash) and the hypotenuse (marked with one dash). This is \(HL\) (Hypotenuse - Leg) congruence for right - angled triangles, not \(AAS\).

Step4: Analyze Pair 4

In pair 4, we have sides marked with three dashes (equal) and sides marked with one dash (equal). This is \(SSS\) (Side - Side - Side) congruence, not \(AAS\).

Answer:

2