Question

In parallelogram PQRS, T is the mid-point of PQ and U is the mid point of SR. Prove that PTRU is a parallelogram.

Answer 1

Given:

T is the mid-point of PQ and U is the mid-point of SR.

To prove:

PTRU is a parallelogram

Solution:

As it is given that PQRS is the parallelogram so,

• PQ║RS
• 1/2PQ║1/2RS
• PT║RU

and,

• PQ=RS
• 1/2PQ=1/2RS
• PT=RU

As we know that the line passing through the mid-points of any of the parallelograms is parallel to the opposite sides of the parallelogram.

• TU║RP
• TU=RP

Hence the opposite pair of sides of the parallelogram are parallel and equal to each other.

PTRU is a parallelogram

Hence Proved