Question

what are the corresponding parts of the figures below? select all that apply.
options:
\\(\overline{fg} \cong \overline{kl}\\)
\\(\overline{ef} \cong \overline{jk}\\)
\\(\angle f \cong \angle k\\)
\\(\angle g \cong \angle l\\)

Explanation:

To determine corresponding parts, we analyze the triangles. Both are right triangles (∠F and ∠K are right angles, so ∠F ≅ ∠K). Sides with same tick marks are congruent: \( \overline{EF} \) (1 tick) ≅ \( \overline{JK} \) (1 tick), \( \overline{FG} \) (2 ticks) ≅ \( \overline{KL} \) (2 ticks). Angles at G and L: ∠G (with 1 arc) and ∠L (with 1 arc) are congruent. So all options \( \overline{FG} \cong \overline{KL} \), \( \overline{EF} \cong \overline{JK} \), \( \angle F \cong \angle K \), \( \angle G \cong \angle L \) are correct.

Answer:

\( \overline{FG} \cong \overline{KL} \), \( \overline{EF} \cong \overline{JK} \), \( \angle F \cong \angle K \), \( \angle G \cong \angle L \) (all the given options with checks are correct as they represent corresponding congruent parts of the two triangles based on right angles, tick marks for congruent sides, and arc marks for congruent angles).