Math, asked by adutysprasad, 10 months ago

R and S are the mid-points of opposite sides AB and DC of a parallelogram ABCD. AS and DR are joined intersecting in P; CR and BS are joined intersecting in Q. Show that PQRS is a parallelogram.

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Answered by Anonymous
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Shivam0011

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Given: X and Y are the mid-points of opposite sides AB and DC of a parallelogram ABCD.

AX = XB and DY = YC

To Prove: PXQY is a parallelogram.

Proof: AB = DC

... AB =  DC

XB = DY......(i)

Also AB ïï DC...... (opp. sides of a ïïgm)

XB ïï DY.....(ii)

Since in quadrilateral XBYD, XB = DY and XB ïï DY

... XBYD is a parallelogram.

... DX ïï YB ⇒ PX ïï YQ......(iii)

Similarly we can prove, PY ïï XQ ......(iv)

From (iii) and (iv), we get PXQY is a parallelogram.

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