Question

given: jm bisects ∠j. jm ⊥ kl
prove: △jmk ≅ △jml

Explanation:

Step1: Use the angle - bisector definition

Since \(JM\) bisects \(\angle J\), we have \(\angle KJM=\angle LJM\).

Step2: Use the right - angle information

We know that \(\angle JMK = 90^{\circ}\) and \(\angle JML=90^{\circ}\) (given the right - angle marks in the figure), so \(\angle JMK=\angle JML\).

Step3: Use the common side

\(JM = JM\) (common side in both \(\triangle JMK\) and \(\triangle JML\)).

Step4: Apply the Angle - Angle - Side (AAS) congruence criterion

In \(\triangle JMK\) and \(\triangle JML\), we have \(\angle KJM=\angle LJM\) (from step 1), \(\angle JMK=\angle JML\) (from step 2), and \(JM = JM\) (from step 3). By the AAS (Angle - Angle - Side) congruence criterion, \(\triangle JMK\cong\triangle JML\).

Answer:

\(\triangle JMK\cong\triangle JML\) (by AAS congruence criterion)