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 ar(ywz)=ar(xwz).
Dear Student,
Consider the figure as given below:
Given: PQRS is a parallelogram. X and Y are midpoints of PQ and RS respectively.
To Prove:
Construction: Join WZ.
Proof: PQRS is a parallelogram.
X and Y are midpoints of PQ and RS respectively and PQ = RS.
Since, one opposite side is parallel and equal so, PXRY is a parallelogram.
Similarly, XQYS is a parallelogram.
YWXZ is a parallelogram.
As, WZ is a diagonal and a diagonal divides the paralellogram in two congruent triangles.
Hence, proved.
Regards,
Consider the figure as given below:
Given: PQRS is a parallelogram. X and Y are midpoints of PQ and RS respectively.
To Prove:
Construction: Join WZ.
Proof: PQRS is a parallelogram.
X and Y are midpoints of PQ and RS respectively and PQ = RS.
Since, one opposite side is parallel and equal so, PXRY is a parallelogram.
Similarly, XQYS is a parallelogram.
YWXZ is a parallelogram.
As, WZ is a diagonal and a diagonal divides the paralellogram in two congruent triangles.
Hence, proved.
Regards,