Question

1. $\triangle fgh sim \triangle jkh$

$angle f cong angle$ answer
$angle g cong angle$ answer
$angle h cong angle$ answer
$fg/$ answer $= $ answer $/ kh = fh/$ answer

Explanation:

Step1: Use the property of similar triangles

When \(\triangle FGH\sim\triangle JKH\), corresponding angles are equal.
So, \(\angle F\cong\angle J\) (corresponding angles of similar triangles).

Step2: Another pair of corresponding angles

\(\angle G\cong\angle K\) (corresponding angles of similar triangles).

Step3: Vertical angles

\(\angle FHG\) and \(\angle JHK\) are vertical angles, so \(\angle H\cong\angle H\) (vertical angles are congruent).

Step4: Corresponding sides

For similar triangles \(\triangle FGH\) and \(\triangle JKH\), the ratio of corresponding sides is equal. So, \(\frac{FG}{JK}=\frac{FH}{JH}=\frac{GH}{KH}\)

Answer:

\(\angle F\cong \angle J\), \(\angle G\cong\angle K\), \(\angle H\cong\angle H\), \(\frac{FG}{JK}=\frac{FH}{JH}=\frac{GH}{KH}\)