Question

question 2 of 10
which of the following are right triangle congruence theorems?
check all that apply.
a. leg - angle (la)
b. leg - leg (ll)
c. hypotenuse - angle (ha)
d. hypotenuse - leg (hl)

Explanation:

• Leg - angle (LA): If a leg and an acute angle of one right - triangle are congruent to the corresponding leg and acute angle of another right - triangle, then the two right - triangles are congruent. This is based on the AAS (Angle - Angle - Side) congruence criterion (since in a right - triangle, we already know one right angle).
• 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 SAS (Side - Angle - Side) congruence criterion (the right angle is the included angle between the two legs).
• Hypotenuse - angle (HA): If the hypotenuse and an acute angle of one right - triangle are congruent to the hypotenuse and an acute angle of another right - triangle, then the two right - triangles are congruent. This is based on the AAS (Angle - Angle - Side) congruence criterion.
• 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 criterion for right - triangles.

Answer:

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