Question

The HA congruence theorem for right triangles is a special case of the _____. A. SAS postulate B. ASA postulate C. AAS theorem D. SSS postulate

Answer 1

Option C.

Explanation:

According to the HA congruence theorem, two right triangles are congruent if

1. Their hypotenuse are congruent.

2. An acute angle of one triangle is congruent to the corresponding acute angle of another triangle.

It means two corresponding angles are congruent (One is right and another is acute angle) and one corresponding side of each triangle is congruent.

According to AAS congruence theorem, two triangles are congruent if

1. Two corresponding angles are congruent.

2. Any non-included side of one triangle is congruent to the corresponding side.

The HA congruence theorem for right triangles is a special case of the AAS theorem.

Therefore, the correct option is C.

Answer 2

Answer: C. AAS theorem

Explanation:

The HA congruence theorem for right triangles says that if the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another right triangle then the two triangles are congruent.

AAS theorem says that if two angles and any side of a triangle are congruent to two angles and any side of another triangle, then the triangles are congruent.

Hence, the HA congruence theorem for right triangles is a special case of the AAS theorem.