In rectangle ABCD, the midpoints of the sides AB, BC, CD and DA are P, Q, R and S respectively. If the range of ABCD and PQRS is 40 cm and 32 cm respectively, what is the area of PQRS?
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8th
Maths
Understanding Quadrilaterals
Some Special Parallelograms
ABCD is a rectangle and P, ...
MATHS
ABCD is a rectangle and P, Q, R and S are mid-points of the side AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.
December 20, 2019Indulekha Gulwani
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Join DB and AC such that two triangles ADB and DBC are formed.
We know that the line joining the midpoints of the two sides of triangle is parallel to the third side and is of half the measure of third side.
Here in triangle ADB P and S are the midpoints of AB and AD respectively,hence PS∥DB also PS=21DB..................1
Similarly,RQ∥DB also RQ=21DB..................2
PQ∥AC also PQ=21AC....................3
SR∥AC also SR=21AC......................4
From equation 1 and 2 we get PS∥RQ and PS=RQ
And from equation 3 and 4 we get PQ∥SR and PQ=SR
Therefore, PQRS is a rhombus.