Question

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

reason

1. given
2. given

3.

1. definition of midpoint
2. sas

Explanation:

Step1: Recall mid - point property

Since K is the mid - point of $\overline{JN}$, by the definition of a mid - point, a mid - point divides a line segment into two congruent segments. So $\overline{JK}\cong\overline{NK}$.

Step2: Use side - angle - side (SAS) postulate

We have $\overline{JL}\cong\overline{NM}$ (given), $\overline{JK}\cong\overline{NK}$ (from mid - point property), and $\angle JKL\cong\angle NKM$ (vertically opposite angles). By the Side - Angle - Side (SAS) postulate, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. So $\triangle JKL\cong\triangle NKM$.

Answer:

1. Definition of Midpoint
2. SAS