CBSE Class 9 Answered
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 | 04 Jun, 2014, 01:23: PM
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 | 04 Jun, 2014, 03:23: PM
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