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Show that the quadrilateral formed by joining the mid-points of the sides of a rhombus taken in order, form a rectangle.

Asked by Topperlearning User 4th June 2014, 1:23 PM
Answered by Expert
Answer:

Let ABCD be a rhombus and P, Q, R and S be the mid-points of sides AB, BC, CD and DA respectively.

In ABD and BDC we have

From (i) and (ii) we get

PQRS is a ||gm

As diagonals of a rhombus bisect each other at right angles.

AC BD

Since SP||BD, PQ||AC and AC BD

From above results, we have

||gm PQRS is a rectangle.

Answered by Expert 4th June 2014, 3:23 PM
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