Question

in the figure shown, \\( \triangle fgh \sim \triangle jkl \\). select all pairs of congruent angles. \\( \square \\) a) \\( \angle f \cong \angle j \\) \\( \square \\) b) \\( \angle f \cong \angle k \\) \\( \square \\) c) \\( \angle g \cong \angle k \\) \\( \square \\) d) \\( \angle h \cong \angle l \\) \\( \square \\) e) \\( \angle g \cong \angle j \\)

Explanation:

Step1: Recall the property of similar triangles

If \(\triangle FGH\sim\triangle JKL\), then corresponding angles are congruent. That is \(\angle F\) corresponds to \(\angle J\), \(\angle G\) corresponds to \(\angle K\), and \(\angle H\) corresponds to \(\angle L\).

Step2: Check each option

• Option A: \(\angle F\) and \(\angle J\) are corresponding angles. So \(\angle F\cong\angle J\) is correct.
• Option B: \(\angle F\) and \(\angle K\) are not corresponding angles. So \(\angle F\cong\angle K\) is incorrect.
• Option C: \(\angle G\) and \(\angle K\) are corresponding angles. So \(\angle G\cong\angle K\) is correct.
• Option D: \(\angle H\) and \(\angle L\) are corresponding angles. So \(\angle H\cong\angle L\) is correct.
• Option E: \(\angle G\) and \(\angle L\) are not corresponding angles. So \(\angle G\cong\angle L\) is incorrect.

Answer:

A. \(\angle F\cong\angle J\), C. \(\angle G\cong\angle K\), D. \(\angle H\cong\angle L\)