Question

which of the following item sets show two triangles that can be proved congruent?

Explanation:

Step1: Recall congruence criteria

Triangles can be proven congruent by 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 Option (1)

There is not enough information provided (only one side and one non - included angle marked), so we can't prove congruence.

Step3: Analyze Option (2)

We have two angles and the included side marked equal, which satisfies the ASA congruence criterion. So the two triangles in Option (2) can be proven congruent.

Step4: Analyze Option (3)

There is not enough information provided (only two sides of right - triangles marked, no information about hypotenuse or other angles), so we can't prove congruence.

Step5: Analyze Option (4)

There is not enough information provided (only one side and one non - included angle marked), so we can't prove congruence.

Answer:

(2)