Answer:
[tex]\overline {PM} \cong \overline {ON}[/tex] because they are opposite sides of a parallelogram.
Step-by-step explanation:
First of all, let us have a look at the definition of a parallelogram.
A parallelogram is a closed 4 sided figure (i.e. a quadrilateral) made up with two pairs of straight lines such that the two pairs are parallel and equal to each other.
For example, let us consider a quadrilateral ABCD as attached in the diagram in answer area.
The two pair of lines are:
AB, DC and BC, AD
For ABCD to be a parallelogram, the lines
AB and DC must be parallel to each other and AB = DC
AND
BC and AD must be parallel to each other and BC = DA
------------------------------
In the given question, we are given that the quadrilateral MNOP is a parallelogram.
The two pairs opposite lines are OP, NM and PM, ON.
As per the definition of a parallelogram,
OP and NM must be parallel and equal to each other.
AND
PM and ON must be parallel and equal to each other.
[tex]\therefore[/tex] [tex]\overline {PM} \cong \overline {ON}[/tex].
Hence proved.
