Question

1. a) aas b) hl c) not enough information d) asa

Explanation:

Step1: Recall triangle congruence criteria

• AAS (Angle - Angle - Side): Two angles and a non - included side of one triangle are equal to the corresponding two angles and non - included side of another triangle.
• HL (Hypotenuse - Leg): Applies only to right - angled triangles.
• ASA (Angle - Side - Angle): Two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.

Step2: Analyze the given figure

In the given figure (a parallelogram divided into two triangles by a diagonal), we have two pairs of angles (marked with red arcs) equal. The side (the diagonal) is common (a non - included side for the pairs of angles). So, it satisfies the AAS (Angle - Angle - Side) congruence criterion.

Answer:

A. AAS