Chapter 5.2, Problem 24WE

To determine

To prove: $LMNO$ is a $▱$ .

Explanation of Solution

Given Information:

Given figure,

  

Plane $X\parallel$ plane $Y$ ;

  $\overline{LM}\cong \overline{ON}$

Calculation:

From the figure, one can easily note that $LM$ and $ON$ are lines are on plane $X$ and $Y$ respectively.

Then $LM\parallel X$ and $ON\parallel Y$ .

It is given that $X\parallel Y$ .

Thus, it can be concluded that $LM\parallel ON$ .

This implies that,

  $LM\parallel ON$ and $LM\cong ON$

Our conclusion is in a quadrilateral $LMNO$ one pair opposite side is equal and parallel.

Therefore, it is proved that $LMNO$ is a parallelogram.