Prove that The line segment joining …
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Sia ? 6 years, 6 months ago
Given: ABCD is a quadrilateral. P, Q, R and S are the mid-points of the consecutive sides AB, BC, CD and DA respectively.
To prove: PQRS is a parallelogram.
Construction: Join BD.
Proof : In {tex}\triangle{/tex}CBD,
Q is the mid-point of BC and R is the mid-points of CD.
{tex}\triangle{/tex} QR || BD and QR = {tex}\frac{1}{2}{/tex} BD ...(1)
In {tex}\triangle{/tex}ABD,
As P is the mid-point of AB and S is the mid-point of AD.
{tex}\therefore{/tex} PS || BD and PS = {tex}\frac{1}{2}{/tex} BD ....(2)
QR = PS and QR || PS ...[From (1) and (2)]
Thus a pair of opp. sides of PQRS are parallel and equal.
PQRS is a parallelogram
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