PQRS is a parallelogram. X and Y are mid-points of sides PQ and RS respectively. If W and Z are points on intersection of SX & PY and XR & YQ respectively, then show that area (triangle YWZ) = area (triangle XWZ)
Answers
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Area (triangle YWZ) = area (triangle XWZ)
Step-by-step explanation:
PQRS is a parallelogram. X and Y are mid-points of sides PQ and RS respectively
PX = QX = PQ/2
SY = RY = RS/2
PQ = RS (opposite sides of parallelogram)
=> PX = RY & QX = SY
in Δ PSY & Δ RQY
PS = QR (opposite sides of parallelogram)
SY = QX
∠PSY = ∠RQS ( opposite angles of parallelogram)
=> Δ PSY ≅ Δ RQY
=> PY = RX
Simialrly we can show
SX = YQ
if we see PXRY
PX = YR
PY = RZ
PX ║ RY (as PQ ║ RS and X and Y lies on PQ & RS)
=> PXRY is a parallelogram
Similarly
XQYS is a parallelogram
= WX ║ YZ & YW ║ XZ
=> XZYW is a parallelogram
WZ is a diagonal
diagonal of parallelogram Divide it into two equal area triangle
=> area (triangle YWZ) = area (triangle XWZ)
QED
proved
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