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.
Answers
Answered by
5
Answer:
Add your answer and earn points.
THE BRAINLIEST ANSWER!
Shivam0011
Shivam0011Helping Hand
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.
Similar questions