Question

Which triangles could you use the HL Theorem to prove that triangle 1 is congruent to triangle 2?

Answer 1

Answer: D) III only

With figure I, we can't use HL (hypotenuse leg) theorem because we don't know if the two hypotenuses are the same length. We know that one pair of legs (the vertical legs) are congruent, but we don't have enough info

With figure II, we have two pairs of congruent legs. The tickmarks tell us this. However we don't know if the hypotenuses are congruent. Note: we can use the LL (leg leg) theorem, which is related to the HL theorem, but that's not what the teacher wants

Figure III is the only figure where we know that a pair of hypotenuses are the same length as shown by the similar tickmarks. The vertical legs are congruent as well for the upper pair of triangles. We have enough info to use HL.