Question

try it using the sas congruence theorem given: $overline{jk} parallel overline{lm}$, $overline{jk} cong overline{lm}$, l is the midpoint of $overline{jn}$. prove: $\triangle jlk cong \triangle lnm$ diagram of triangles with vertices j, k, l, m, n statements reasons 1. $overline{jk} parallel overline{lm}$ 1. given 2. $overline{jk} cong overline{lm}$ 2. given 3. l is the midpoint of $overline{jn}$. 3. given 4. $overline{jl} cong overline{ln}$ 4. def. of midpoint correct! assemble the next statement.

Explanation:

Step1: Identify Corresponding Angles

Since \(\overline{JK} \parallel \overline{LM}\), by the Corresponding Angles Theorem, \(\angle J \cong \angle NLM\).

Step2: Apply SAS Congruence

We have \(\overline{JK} \cong \overline{LM}\) (given), \(\overline{JL} \cong \overline{LN}\) (def. of midpoint), and \(\angle J \cong \angle NLM\) (corresponding angles). So, the next statement is \(\triangle JLK \cong \triangle LNM\) by SAS.

Answer:

The next statement is \(\boldsymbol{\triangle JLK \cong \triangle LNM}\) with the reason "SAS (Side - Angle - Side) Congruence Theorem" (using the sides \(\overline{JK} \cong \overline{LM}\), \(\overline{JL} \cong \overline{LN}\) and the included angle \(\angle J \cong \angle NLM\)).