Question

PQRS is a rectangle and D,E,F and G are midpoints of the sides PQ,QR,RS and PS

respectively. Show that quadrilateral DEFG is a rhombus.​

Answer 1

Given  PQRS is a rectangle and D,E,F and G are midpoints of the sides PQ,QR,RS and PS  respectively.

To Find : Show that quadrilateral DEFG is a rhombus.​

Solution:

PQRS is a rectangle

=> PR = QS   ( diagonal of rectangle are equal )

line joining the mid-point of two sides of a triangle is equal to half the length of the third side

D,E,F and G are midpoints of the sides PQ,QR,RS and PS

=> DE = PR/2

   FG = PR/2

   EF = QS/2

   DG = QD/2

PR = QS

Hence PR/2 =  QS/2

=> DE = FG = EF = DG

Hence DEFG is a rhombus.​    ( rhombus has all 4 sides equal )

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