Q. 164.6( 9 Votes )

ABCD is a quadril

Answer :

Given: AD = BC

P, Q, R and S are the midpoints of AB, AC, CD and BD respectively.


So in ∆ABC, if P and Q are midpoints of AB and A respectively PQ BC


And PQ = (1/2)BC …(i)


Similarly in ∆ADC,


QR = (1/2)AD …(ii)


In ∆BCD,


SR = (1/2)BC …(iii)


In ∆ABD,


PS = (1/2)AD = (1/2)BC [ AD = BC]


Using equations (i), (ii), (iii) & (iv), we get


PQ = QR = SR = PS


All these sides are equal.


PQRS is a rhombus.


Hence, shown that PQRS is a rhombus.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses