Question

1. which additional congruence statement could you use to prove that △cab≅△cad by hl?

○ (overline{bc}congoverline{cd})
○ (overline{bd}congoverline{bd})
○ (overline{ab}congoverline{ad})
○ (overline{ac}congoverline{ac})

Explanation:

Step1: Recall HL - Hypotenuse - Leg

The HL (Hypotenuse - Leg) congruence theorem for right - triangles states that if the hypotenuse and one leg of a right - triangle are congruent to the hypotenuse and one leg of another right - triangle, then the two right - triangles are congruent. In right - triangles $\triangle CAB$ and $\triangle CAD$, $\angle ACB=\angle ACD = 90^{\circ}$ and $AC$ is common (reflexive property).

Step2: Identify the hypotenuse

We need to show that the hypotenuses of the two right - triangles are congruent. The hypotenuse of $\triangle CAB$ is $AB$ and the hypotenuse of $\triangle CAD$ is $AD$. For $\triangle CAB\cong\triangle CAD$ by HL, we need $\overline{AB}\cong\overline{AD}$.

Answer:

$\overline{AB}\cong\overline{AD}$