1.

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»

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


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