Question

in the diagram below, \\( \angle j i k \cong \angle m l k \\). enter segments in the blanks provided that would result in a true equation.
answer
\\( \frac { l j } { j k } = \frac { k i } { \square } \\)

Explanation:

Step1: Identify similar triangles

Since \(\angle JIK\cong\angle MLK\) and \(\angle IKJ=\angle LKM\) (vertical angles are congruent), by the AA (Angle - Angle) similarity criterion, \(\triangle IJK\sim\triangle MLK\).

Step2: Use the property of similar triangles

For similar triangles \(\triangle IJK\) and \(\triangle MLK\), the ratios of corresponding sides are equal. That is \(\frac{IJ}{JK}=\frac{ML}{LK}\).

Answer:

\(\frac{IJ}{JK}=\frac{ML}{LK}\)