Question

1. which additional congruence statement could you use to prove that ( \triangle cabcong\triangle cad ) by hl? ( overline{ac}congoverline{ac} ) ( overline{bd}congoverline{bd} ) ( overline{ab}congoverline{ad} ) ( overline{bc}congoverline{cd} )

Explanation:

Step1: Recall the HL (Hypotenuse - Leg) Congruence Theorem

The HL 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. In \(\triangle CAB\) and \(\triangle CAD\), \(\angle ACB=\angle ACD = 90^{\circ}\) (right angles), and \(AC = AC\) (common leg).

Step2: Identify the hypotenuse for each right - triangle

The hypotenuse of \(\triangle CAB\) is \(AB\), and the hypotenuse of \(\triangle CAD\) is \(AD\). For the HL theorem to apply, we need the hypotenuses to be congruent.

Answer:

\(\overline{AB}\cong\overline{AD}\)