Question

it is given that \\( \triangle a b c \\) and \\( \triangle d e f \\) are both right triangles and have exactly one right angle. all right angles are congruent, so \\( \angle c \cong \angle f \\).
it is given that \\( \angle b \cong \angle e \\) and that \\( \overline{a b} \cong \overline{d e} \\).
\\( \overline{a b} \\) is an included side between \\( \angle b \\) and \\( \angle c \\).
\\( \overline{d e} \\) is an included side between \\( \angle e \\) and \\( \angle f \\).
through the congruencies of, \\( \angle b \cong \angle e \\), and \\( \overline{a b} \cong \overline{d e} \\), it follows that \\( \triangle a b c \cong \triangle d \\) theorem.

Explanation:

Step1: Recall the ASA (Angle - Side - Angle) Congruence Theorem

The ASA theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Step2: Identify the congruent angles and side

We are given that \(\angle B\cong\angle E\), \(\overline{AB}\cong\overline{DE}\), and from the fact that all right - angles are congruent \(\angle C\cong\angle F\).

Answer:

\(\angle C\cong\angle F\)