Question

given lm ≅ on and lo ≅ mn. prove lmno is a parallelogram. assemble the proof by dragging tiles to the statements and reasons columns.

Explanation:

Step1: Consider triangles

In $\triangle LMN$ and $\triangle ONM$, we have $LM = ON$ (given), $LO = MN$ (given), and $MN=LO$ (common - side).

Step2: Prove triangle congruence

By SSS (Side - Side - Side) congruence criterion, $\triangle LMN\cong\triangle ONM$.

Step3: Find equal angles

Since $\triangle LMN\cong\triangle ONM$, $\angle LMN=\angle ONM$ and $\angle MLN=\angle NOM$ (corresponding parts of congruent triangles are equal).

Step4: Use angle - side relationship

Because $\angle LMN=\angle ONM$, $LM\parallel ON$ (alternate interior angles are equal, so lines are parallel). Also, since $\angle MLN=\angle NOM$, $LO\parallel MN$.

Step5: Define parallelogram

A quadrilateral with both pairs of opposite sides parallel is a parallelogram. So, $LMNO$ is a parallelogram.

Answer:

$LMNO$ is a parallelogram.