Question

given: jk || lm, jk ≅ lm. l is the mid - point of jn. prove: △jlk ≅ △lnm. assemble the proof by dragging tiles to the statements and reasons columns.

Explanation:

Step1: Identify given sides

$\overline{JK} \cong \overline{LM}$ (Given)

Step2: Midpoint gives congruent segments

$\overline{JL} \cong \overline{NL}$ (L is midpoint of $\overline{JN}$)

Step3: Parallel lines give congruent angles

$\angle J \cong \angle N$ (Alternate Interior Angles, $\overline{JK} \parallel \overline{LM}$)

Step4: Apply SAS Congruence

$\triangle JLK \cong \triangle NLM$ (SAS: $\overline{JK} \cong \overline{LM}$, $\angle J \cong \angle N$, $\overline{JL} \cong \overline{NL}$)

Answer:

$\triangle JLK \cong \triangle NLM$ by SAS Congruence Theorem.