Question

For the following right triangles:

AC≅DF
What else do we need to know to prove that the triangles are congruent by HL?
A. B. C. CB≅FE
D. AB≅DE

Answer 1

Let us first define Hypotenuse Leg (HL) congruence theorem:

If the hypotenuse and one leg of a right angle are congruent to the hypotenuse and one leg of the another triangle, then the triangles are congruent.

Given ACB and DFE are right triangles.

To prove ΔACB ≅ ΔDFE:

In ΔACB and ΔDFE,

AC ≅ DF (one side)

∠ACB ≅ ∠DFE (right angles)

AB ≅ DE (hypotenuse)

∴ ΔACB ≅ ΔDFE by HL theorem.