Question

given: ∠k ≅ ∠m, l is midpoint of km
prove: l is midpoint of jp
5)

Explanation:

Step1: Vertical angles

Vertical angles are equal. So, $\angle KLJ=\angle ML P$.

Step2: Congruent triangles

Given $\angle K\cong\angle M$, and the sides (marked as equal in the figure). By the Angle - Side - Angle (ASA) congruence criterion, $\triangle KLJ\cong\triangle ML P$.

Step3: Mid - point property

Since $\triangle KLJ\cong\triangle ML P$, then $JL = PL$. So, $L$ is the mid - point of $\overline{JP}$.

Answer:

$L$ is the mid - point of $\overline{JP}$ is proved as above.