Question

decide whether enough information is given to prove that $\triangle abc \cong \triangle fed$ using the hl congruence theorem. explain

$\angle b$ and $\underline{\quad\quad}$ are right angles, $\overline{ab} \cong \underline{\quad\quad}$, and $\overline{ac} \cong \underline{\quad\quad}$. so, the triangles $\underline{\quad\quad}$ be proven congruent

using the hl congruence theorem because $\underline{\quad\quad}$

Explanation:

1. First, identify the right angles in each triangle: $\triangle ABC$ has right angle $\angle B$, and $\triangle FED$ has right angle $\angle E$.
2. Match the marked congruent sides: the leg $\overline{AB}$ corresponds to the leg $\overline{FE}$, and the hypotenuse $\overline{AC}$ corresponds to the hypotenuse $\overline{FD}$.
3. The HL Congruence Theorem requires one pair of congruent legs and one pair of congruent hypotenuses in right triangles, which is satisfied here.

Answer:

$\angle B$ and $\boldsymbol{\angle E}$ are right angles, $\overline{AB} \cong \boldsymbol{\overline{FE}}$, and $\overline{AC} \cong \boldsymbol{\overline{FD}}$. So, the triangles $\boldsymbol{can}$ be proven congruent using the HL Congruence Theorem because $\boldsymbol{the information is sufficient}$.