Question

Ashley says that the CDE ≅ FGH 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

Ashley is incorrect. CDE ≅ FGH by the LL theorem.

Explanation:

In the given picture, there are two triangles ΔCDE and ΔFHG which are right triangle [Since ∠D=∠H=90°].

In ΔCDE and ΔFHG.

CD=HF

DE=HG

∠D=∠H=90°

Therefore, by LL theorem,

ΔCDE ≅ ΔFHG.

Therefore, Ashley is incorrect. CDE ≅ FGH by the LL theorem.

LL theorem says that if the legs of one right triangle are congruent to the legs of other right triangle, then the triangles are said to be congruent.

The HL Theorem says if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of other right triangle, then the triangles are said to be congruent.

Answer 2

I hope this helps you