Question

1. which pair of triangles are congruent based on the given information?

Explanation:

Step1: Analyze the first option

In the first option, the angles of the two triangles are not matching in a way that would satisfy a congruence criterion (like ASA, SAS, SSS).

Step2: Analyze the second option

In the second option, only right - angle and one acute angle are given. There is no information about the sides. So, we cannot confirm congruence.

Step3: Analyze the third option

In the third option, for \(\triangle MAT\) and \(\triangle MHT\):

• \(MA = MH\) (given as equal segments)
• \(MT=MT\) (common side)
• \(AT = HT\) (given as equal segments)

By SSS (Side - Side - Side) congruence criterion, \(\triangle MAT\cong\triangle MHT\)

Answer:

The pair of triangles \(\triangle MAT\) and \(\triangle MHT\) (the third option) are congruent.