Math, asked by 8076095263, 1 year ago

PQRS is a parallelogram .Xand Y are midpoints of sides PQ and RS respectively. If W and Z are points on intersection of SX&PY and XR& YQ respectively, then show that ar(∆YWZ)=ar(∆XWZ)

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Answered by dhruvsh1
4
PQRS is a llgm
and X & Y are midpoint of sides PQ AND RS respectively.
in quad. XQYS,
SY = QX AND ALSO SY ll QX
therefore quad XQYS is a llgm.

In quad.PXRY ,
PX = YR & PX ll YR.
therefore quad PXRY is a llgm.
also in quadrilateral XZYW
XW ll YZ
YW ll ZX
therefore XZYW is a llgm.
therefore ar(YWZ) = ar(XWZ).
as WZ is the diagonal of the parellelogram
& we know that the diagonal of a llgm divides it into two triangles of equal areas.
Answered by sawantnitesh9792234
0

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