Question

two sides and the non - included right angle of one right triangle are congruent to the corresponding parts of another right triangle. which congruence theorem can be used to prove that the triangles are congruent? aas hl sas sss

Explanation:

• AAS (Angle - Angle - Side):
• In a right - triangle, we already have one right - angle (\(90^{\circ}\)). If we have another non - included angle (given) and two sides. For right - triangles, when we consider the AAS congruence, we know that in a triangle, the sum of angles is \(180^{\circ}\). In a right - triangle, if we know one non - right angle (\(\angle A\)) and a right angle (\(\angle C = 90^{\circ}\)), then \(\angle B=180^{\circ}-\angle A - 90^{\circ}\). If two sides and a non - included angle (where one of the angles is the right - angle) are congruent, we can use AAS.
• HL (Hypotenuse - Leg): Requires the hypotenuse and a leg, but the problem just says two sides (not specifically hypotenuse and leg) and a non - included right - angle.
• SAS (Side - Angle - Side): Requires the angle to be included between the two sides. Here, the right - angle is non - included.
• SSS (Side - Side - Side): Requires all three sides to be congruent. The problem only mentions two sides.

Answer:

A. AAS