Question

Given: $\mathrm{Plane}\mathrm{X}\parallel \mathrm{Plane}\mathrm{Y};\overline{\mathrm{LM}}\cong \overline{\mathrm{ON}}$

Prove: LMNO is a parallelogram.

Short answer

As LM and ON are parallel and congruent to each other, LMNO is a parallelogram.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Description of step.

From the given diagram it can be noticed that LM and ON are the lines lying on plane X and plane Y respectively.

As plane X is parallel to plane Y and lines LM and ON are the lines lying on plane X and plane Y respectively.

Therefore, it can be said that the lines LM and ON are parallel to each other.

Step 3. Description of step.

It is being given that $\overline{LM}\cong \overline{ON}$.

Therefore, it can be noticed that LM and ON are parallel and congruent to each other.

If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.

Therefore, as LM and ON are parallel and congruent to each other, LMNO is a parallelogram.