Question

1. state the postulate by which the triangles are congruent.

Explanation:

Step1: Recall congruent triangle postulates

There are several postulates for triangle congruence: 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 the given triangles

Looking at the triangles, we can see that two angles and a non - included side are marked as equal.

Step3: Identify the postulate

The AAS (Angle - Angle - Side) postulate states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.

Answer:

The triangles are congruent by the AAS (Angle - Angle - Side) postulate.