Question

IF AED AND CED ARE BOTH RIGHT TRIANGLES, what triangle congruence could be used to prove that the two triangles are congruent?

Answer 1

I would go with SAS-Side Angle Side. I was stuck on that one too until i looked at it closely and looked at the review notes.

Explanation:

Answer 2

Leg-Acute (LA) Angle Theorem.

Explanation:

We can use the postulate Leg-Acute Angle theorem to demonstrate the congruence.

This postulate states "if a leg and an acute angle of one triangle are congruent to the corresponding parts of another right triangle, then those two right triangles are congruent".

So, in this case, we have

`ED \cong ED`, by reflexive property, that is, a segment is congruent to itself.

`\angle A \cong \angle C`, by Given.

So, with these two given congruence we demonstrate that
`\triangle AED \cong \triangle CDE`, by Leg-Acute Angle Postulate.

Therefore, the answer is Leg-Acute Angle Postulate.