# ABCD is a parellelogram, X and Y are points on DC and AB such that AY = CX. Prove that XY and BD bisect each other.

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by pravin3103

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by pravin3103

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See the diagram.

Let XY and BD intersect at O.

given that AY=CX

we know that AB= CD

so AB- AY = CD- CX

or BY=DX

In triangle, YOB and XOD,

angle YOB = angle XOD

angle ODX = angle OBY

BY=DX

So both are congruent.

Thus OD = BO

and XO = YO

So they bisect each other.(proved)

Let XY and BD intersect at O.

given that AY=CX

we know that AB= CD

so AB- AY = CD- CX

or BY=DX

In triangle, YOB and XOD,

angle YOB = angle XOD

angle ODX = angle OBY

BY=DX

So both are congruent.

Thus OD = BO

and XO = YO

So they bisect each other.(proved)

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

We know that opposite sides are equal in parellelogram

AB=CD

1/2 AB=1/2 CD

let BD and XY meets at O

in triangle DOX and triangle BOY DX = by proved

angle DOX =angle BOY vertically opposite angle

angle ODX = angle OBY alternate interior angle

therefore triangle DOX is congurant to triangle BOY therefore DO = BO

therefore XY bisects BD

hence proved

AB=CD

1/2 AB=1/2 CD

let BD and XY meets at O

in triangle DOX and triangle BOY DX = by proved

angle DOX =angle BOY vertically opposite angle

angle ODX = angle OBY alternate interior angle

therefore triangle DOX is congurant to triangle BOY therefore DO = BO

therefore XY bisects BD

hence proved