Question

given: $overline{jl}congoverline{nm}$, k is the mid - point of $overline{jn}$ and $overline{lm}$. prove: $\triangle{jkl}cong\triangle{nk m}$
statement

1. $overline{jl}congoverline{nm}$
2. k is the mid - point of $overline{jn}$ and $overline{lm}$
3. $overline{jk}congoverline{nk}$
4. $overline{lk}congoverline{mk}$
5. $\triangle{jkl}cong\triangle{nk m}$

reason

1. given
2. given
3. definition of midpoint
4. sas

5.

Explanation:

Step1: Identify given information

Given $\overline{JL}\cong\overline{NM}$ and $K$ is mid - point of $\overline{JN}$ and $\overline{LM}$.

Step2: Use mid - point property

Since $K$ is the mid - point of $\overline{JN}$, by the definition of a mid - point, $\overline{JK}\cong\overline{NK}$.

Step3: Use mid - point property again

Since $K$ is the mid - point of $\overline{LM}$, by the definition of a mid - point, $\overline{LK}\cong\overline{MK}$.

Step4: Apply congruence criterion

In $\triangle{JKL}$ and $\triangle{NK M}$, we have $\overline{JL}\cong\overline{NM}$, $\overline{JK}\cong\overline{NK}$, $\overline{LK}\cong\overline{MK}$. By the Side - Side - Side (SSS) congruence criterion, $\triangle{JKL}\cong\triangle{NK M}$.

Answer:

1. SSS