Question

question 6 of 10
which of the following are right triangle congruence theorems?
check all that apply.
a. leg - leg (ll)
b. hypotenuse - angle (ha)
c. hypotenuse - leg (hl)
d. leg - angle (la)

Explanation:

• Leg - leg (LL): If the two legs of one right - triangle are congruent to the two legs of another right - triangle, then the two right - triangles are congruent. This is based on the Side - Side - Side (SSS) congruence in a right - triangle context (since the right - angle is already known and the two legs are the sides).
• Hypotenuse - leg (HL): If the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent. This is a special congruence theorem for right - triangles.
• Leg - angle (LA): If a leg and an acute angle of one right - triangle are congruent to a leg and an acute angle of another right - triangle, then the two right - triangles are congruent. This can be thought of in terms of either the Angle - Side - Angle (ASA) or the Angle - Angle - Side (AAS) congruence theorems, with the right - angle being the additional angle.

The "Hypotenuse - angle (HA)" is not a valid right - triangle congruence theorem.

Answer:

A. Leg - leg (LL), C. Hypotenuse - leg (HL), D. Leg - angle (LA)