Question

state the third congruence that must be given to prove that \\( \triangle abc \cong \triangle def \\) using hl congruence theorem. \\( \overline{ac} \cong \overline{df} \\) \\( \angle a \\) is a right angle \\( \angle a \cong \angle d \\)

Explanation:

Step1: Recall HL Congruence Theorem

The HL (Hypotenuse - Leg) Congruence Theorem states that if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the two right triangles are congruent.

Step2: Identify the required elements

We already have \(\overline{AC}\cong\overline{DF}\) (a leg). For the HL theorem, we need to confirm that both triangles are right - angled. So, we need to know that \(\angle A\) and \(\angle D\) are right angles.

Answer:

\(\angle A\) is a right angle