Question

the hl congruence theorem quick check
consider right triangles $delta abc$ and $delta xyz$. angle $b$ and angle $y$ are congruent. the hypotenuse of each triangle is $overline{ac}$ and $overline{xz}$, and they are congruent. what other corresponding parts must be congruent to show that $delta abccongdelta xyz$ by the hl congruence theorem? (1 point)
$overline{bc}congoverline{xz}$
$overline{ab}congoverline{yz}$
$overline{bc}congoverline{xy}$
$overline{ab}congoverline{xy}$

Explanation:

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. Given that the hypotenuses $\overline{AC}$ and $\overline{XZ}$ are congruent, we need one of the legs to be congruent. Since $\angle B$ and $\angle Y$ are right angles, the legs adjacent to these right angles must be congruent. In $\triangle ABC$, the leg adjacent to $\angle B$ is $\overline{AB}$, and in $\triangle XYZ$, the leg adjacent to $\angle Y$ is $\overline{XY}$.

Answer:

$\overline{AB}\cong\overline{XY}$