Question

consider right triangles $\triangle abc$ and $\triangle xyz$. 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 $\triangle abccong\triangle xyz$ by the hl congruence theorem? (1 point)
$overline{bc}congoverline{xy}$
$overline{ab}congoverline{yz}$
$overline{ab}congoverline{xy}$
$overline{bc}congoverline{xz}$

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 $AC$ and $XZ$ 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 $BC$, and in $\triangle XYZ$, the leg adjacent to $\angle Y$ is $YZ$. So, $BC\cong YZ$ (but this is not an option). The other leg in $\triangle ABC$ is $AB$ and in $\triangle XYZ$ is $XY$. For $\triangle ABC\cong\triangle XYZ$ by HL, we need $AB\cong XY$.

Answer:

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