Question

Could anyone please help me solve this question?

Ashley says that the CDE ≅ FHG by the HL postulate.

In two or more complete sentences, explain why or why not Ashley is correct. Justify your answer using triangle congruency postulates, theorems, and definitions.

Answer 1

HL stands for "hypotenuse leg"

The idea is that if we have a pair of congruent hypotenuses and a pair of congruent legs, then we can prove the right triangles to be congruent.

While we have one pair of legs, we do not have one pair of hypotenuses that are known to be congruent. This is shown by the lack of tick marks on the hypotenuse. Recall that the hypotenuse is the longest side of the right triangle. It is opposite the 90 degree angle always.

So Ashley cannot use HL. Ashley can use LL (leg leg) or she can use SAS (side angle side). In fact, LL is a very special case of SAS where the angle is 90 degrees.