Which triangles could you use the hl theorem to prove that triangle 1 is congruent to triangle 2?

The triangles that we can use the HL Theorem to prove that triangles 1 and 2 are congruent is: D. III only.

What is the HL Congruence Theorem?

The HL Congruence Theorem is used to prove that two right triangles are congruent if they both have a pair of congruent hypotenuses and a pair of congruent legs.

Figure 1 doesn't tell us the hypotenuse lengths.

Figure 2 doesn't show right triangles.

Only Figure 3 shows a two right triangles with marked equal hypotenuses and a shared side length (congruent legs).

Therefore, the triangles that we can use the HL Theorem to prove that triangles 1 and 2 are congruent is: D. III only.

Learn more about HL Theorem on:

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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. 

Yea they are simplyfiy the ratios