how to prove that when all mid points of any quadrilateral are joined they make a parallelogram?

Asked by  | 29th Jan, 2009, 08:50: PM

Expert Answer:

Consider that the quadrilateral is ABCD.

Let P,Q,R,S be the mid points of AB,BC,CD and DA.

Join diagonal AC.

Consider triangle ABC.

Here, P and Q are the mid points of the sides  AB and BC resspectively.

So using the  mid point theorem we can say that PQ is parallel to AC.

Simly,RS can be shown paralle to AC.

So, we have that PQ is parallel to RS (as both are parallel to AC.)

In the same way  you can join diagonal BD and show that QR and SP are both prallel to each other ( as they both can be shown parallel to  BD)

So, we have a quadrilateral PQRS in which both pairs of opp sides are parallel so it becomes a parallelogram.

Answered by  | 29th Jan, 2009, 11:42: PM

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