NCERT Solutions for Class 9 Maths Chapter 8
Important NCERT Questions
Quadrilaterals
NCERT Books for Session 2022-2023
CBSE Board and UP Board Others state Board
EXERCISE 8.2
Page No:150
Questions No:6
Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.
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In ÎACD,
S is mid-point to DA [â” Given]
R is mid-point of DC [â” Given]
Hence, SR â„ AC and SR = (1/2)AC … (1) [â” Mid-point Theorem]
In ÎACD,
P is mid-point of AB [â” Given]
Q is mid-point of BC [â” Given]
Hence, PQ â„ AC and PQ = (1/2) AC …(2) [â” Mid-Point Theorem]
From (1) and (2), we have
PQ â„ SR …(3) [â” PQ â„ AC and SR â„ AC]
and PQ = SR …(4) [â” SR = (1/2)AC and PQ = (1/2)AC]
In quadrilateral PQRS,
PQ â„ SR and PQ = SR [â” From (3) and (4)]
Hence, PQRS is a parallelogram and diagonals of parallelogram bisect each other.
Therefore, SQ and PR bisects each other.