Question

II.
Refer to the adjoining figure, construct a line parallel to AB passing through
the point P. Draw another line parallel to CD also through the point P. Name
the geometrical plane figure so formed.​

Answer 1

Given:

Two line are AB and CD intersect at point R. One point P is given.

To Find:

What will be geometrical plane figure formed. After drawing a line parallel to AB passing through  the point P and draw another line parallel to CD also through the point P.

Solution:

Draw a line XY parallel to line AB through point P:

XY ║ AB        

Draw a line LM parallel to line CD through point P:

LM ║ CD

Line CD and line LM intersect to line AB respectively at point R and S:

Similarly Line CD and line LM intersect to line XY respectively at point Q and P:    

Here we see that a quadrilateral is formed PQRS:

We see that:

RS ║ QP        ...1)

and

RQ ║ SP       ...2)

So quadrilateral PQRS will be a parallelogram because its opposite side are parallel. It is criteria of a parallelogram.