Question

In a parallelogram PQRS, X and Y are the mid points of sides PQ and RS respectively. Show that the line segments PY and XR trisect the diagonal QS.​

Answer 1

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 A PSY & A RQY

PS = QR (opposite sides of parallelogram)

SY = QX

ZPSY = ZRQS (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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