Question

question 3 of 25
which of the following are congruence theorems for right triangles?
check all that apply.

a. ll

b. hl

c. ha

d. hh

e. aa

f. la

Explanation:

• LL (Leg - Leg): If the two legs of one right triangle are equal to the two legs of another right triangle, the triangles are congruent (by SAS, as the right angle is included).
• HL (Hypotenuse - Leg): A special congruence theorem for right triangles where if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, the triangles are congruent.
• HA (Hypotenuse - Angle): If the hypotenuse and an acute angle of one right triangle are equal to the hypotenuse and an acute angle of another right triangle, the triangles are congruent (by AAS, since the right angles are equal).
• LA (Leg - Angle): If one leg and an acute angle of one right triangle are equal to one leg and the corresponding acute angle of another right triangle, the triangles are congruent (by ASA or AAS, considering the right angle).

• HH (Hypotenuse - Hypotenuse): Just having equal hypotenuses is not sufficient for congruence of right triangles, as the legs can be different.
• AA (Angle - Angle): AA is a similarity criterion, not a congruence criterion for triangles (including right triangles). It only shows the triangles are similar, not necessarily congruent.

Answer:

A. LL, B. HL, C. HA, F. LA