Question

the hl congruence theorem quick check
consider right triangles δabc and δxyz. 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 δabc≅δxyz by the hl congruence theorem? (1 point)
(ooverline{ab}congoverline{yz})
(ooverline{bc}congoverline{xz})
(ooverline{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 the corresponding legs to be congruent. Since $\angle B$ and $\angle Y$ are right - angles, the legs adjacent to these right - angles must be congruent. In $\triangle ABC$ and $\triangle XYZ$, the correct pair of corresponding legs is $\overline{AB}$ and $\overline{XY}$.

Answer:

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