Question

given: $overline{jk} cong overline{lm}$, $overline{jm} cong overline{lk}$
prove: $\triangle jkm cong \triangle lmk$

Explanation:

Step1: List given congruent sides

$\overline{JK} \cong \overline{LM}$, $\overline{JM} \cong \overline{LK}$

Step2: Identify common side

$\overline{MK} \cong \overline{MK}$ (Reflexive Property of Congruence)

Step3: Apply SSS congruence rule

All three pairs of corresponding sides of $\triangle JKM$ and $\triangle LMK$ are congruent.

Answer:

$\triangle JKM \cong \triangle LMK$ by the Side-Side-Side (SSS) Triangle Congruence Postulate.