Question

1. which additional congruence statement could you use to prove that $\triangle cabcong\triangle cad$ by hl?

$overline{bd}congoverline{bd}$
$overline{bc}congoverline{cd}$
$overline{ac}congoverline{ac}$
$overline{ab}congoverline{ad}$

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 \(AC\) is a common leg (\(\overline{AC}\cong\overline{AC}\) by the reflexive property).

Step2: Identify the hypotenuse for HL

For the HL theorem to apply to \(\triangle CAB\) and \(\triangle CAD\), we need to show that the hypotenuses are congruent. The hypotenuses of \(\triangle CAB\) and \(\triangle CAD\) are \(AB\) and \(AD\) respectively.

Answer:

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