Question

the congruence statement is \boxed{} you are given that (overline{jk} cong \boxed{} cong overline{lm} cong overline{mj}). also, (overline{jl} cong \boxed{}) by the \boxed{} so, (\triangle jkl cong \boxed{}) by the sss congruence theorem.
options: (overline{jl}), (overline{kl}), (overline{lj}), correct, not correct, (\triangle jml), (\triangle mlj), (\triangle ljm), (\triangle jlm), (\triangle lmj), (\triangle mlj), symmetric property of congruence, reflexive property of congruence, transitive property of congruence

Explanation:

Step1: Identify given congruent sides

From the diagram, $\overline{JK} \cong \overline{LM}$ and $\overline{KL} \cong \overline{MJ}$.

Step2: Identify shared side property

$\overline{JL} \cong \overline{LJ}$ by the Reflexive Property of Congruence.

Step3: Apply SSS Congruence Theorem

Match corresponding sides: $\overline{JK} \cong \overline{LM}$, $\overline{KL} \cong \overline{MJ}$, $\overline{JL} \cong \overline{LJ}$, so $\triangle JKL \cong \triangle LMJ$.

Step4: Verify congruence statement validity

The congruence statement $\triangle JKL \cong \triangle LMJ$ is correct.

Answer:

The congruence statement is $\boldsymbol{\text{correct}}$. You are given that $\overline{JK} \cong \boldsymbol{\overline{LM}}$ and $\overline{KL} \cong \overline{MJ}$. Also, $\overline{JL} \cong \boldsymbol{\overline{LJ}}$ by the $\boldsymbol{\text{Reflexive Property of Congruence}}$. So, $\triangle JKL \cong \boldsymbol{\triangle LMJ}$ by the SSS Congruence Theorem.