Question

given: (overline{lm}congoverline{on}) and (overline{lo}congoverline{mn}) prove: lmno is a parallelogram assemble the proof by dragging tiles to the statements and reasons columns.

Explanation:

Step1: Congruent segments

$\overline{LM}\cong\overline{ON}$, $\overline{LO}\cong\overline{MN}$ (Given)

Step2: Common side

$\overline{LN}\cong\overline{LN}$ (Reflexive property of congruence)

Step3: Triangle congruence

$\triangle LMN\cong\triangle NOL$ (SSS - Side - Side - Side congruence criterion)

Step4: Alternate interior angles

$\angle NLM\cong\angle ONL$, $\angle MLN\cong\angle OLN$ (Corresponding parts of congruent triangles are congruent)

Step5: Parallel lines

$LM\parallel ON$, $LO\parallel MN$ (If alternate interior angles are congruent, then the lines are parallel)

Step6: Parallelogram definition

$LMNO$ is a parallelogram (A quadrilateral with both pairs of opposite sides parallel is a parallelogram)

Answer:

The proof is assembled as above to show that \(LMNO\) is a parallelogram.