Question

Which statement can be used to prove that the two triangles are congruent?

A: the HL Theorem

B: the Angle-Side-Angle Postulate (ASA)

C: the Angle-Angle-Side Theorem (AAS)


D: the SAS Postulate

Answer 1

The SAS postulate

Explanation:

• Longer lengths of the two triangles are equal (S)

• The triangles are reflected about the line where their equal hyputenuses meet (S)
• The right angle of one triengle is equal to the right angle of the other triengle (A)

Thus the two triangles are congruent as evidenced by the SAS postulate.

Answer 2

HL Theorem

Explanation:

Here, we see that both triangles have a right angle, making them right triangles. We know that the hypotenuse must be equivalent, as it is the same line. Furthermore, we see that one of the legs from each triangle are equivalent. Therefore, we can use HL Theorem to prove these triangles are equal.