CBSE Class 9 Answered
Show that the line segments joining the mid points of the opposite sides of a quadrilateral bisect each other.
Asked by Topperlearning User | 17 Aug, 2017, 07:23: AM
Expert Answer
ABCD is a quadrilateral such that P, Q, R and s are the mid points of sides AB, BC, CD and DA respectively.
In 
ABC, P and Q are the mid points of sides AB and BC respectively.
ABC, P and Q are the mid points of sides AB and BC respectively.PQ 
AC and PQ = 
AC
AC and PQ = ACSimilarly, RS 
AC and RS = 
AC
AC and RS = AC
PQ 
RS and PQ = RSSimilarly, PQ QR and PQ = QR
QR and PQ = QRHence, PQRS is a parallelogram.
Since the diagonals of a parallelogram bisect each other,
PR and QS bisect each other.
Answered by | 17 Aug, 2017, 09:23: AM
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