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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)

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