Question

how are these triangles congruent? hl sss aas asa

Explanation:

Step1: Recall congruence criteria

• HL (Hypotenuse - Leg): For right - angled triangles, if the hypotenuse and one leg are equal.
• SSS (Side - Side - Side): All three sides of one triangle are equal to the three sides of another triangle.
• AAS (Angle - Angle - Side): Two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle.
• ASA (Angle - Side - Angle): Two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

Step2: Analyze the given triangles

• The triangles are right - angled (right angles are given).
• We have two pairs of non - right angles equal (marked in the figure) and a common side (the side \(AC\)).
• In the case of right - angled triangles, when we have two angles (one right angle and one non - right angle) and a non - included side (the common side \(AC\) which is not between the two non - right angles in the context of the congruence of the two triangles), the congruence criterion is AAS.

Answer:

AAS