Question

Points X and Y lie on opposite sides AB and CD respectively of a parallelogram ABCD such that AX= CY. show that AC and XY bisect each other. Plsss provide d figure too.

Answer 1

We know,
In ΔAXO and ΔCYO ,
AX = CY
<XAO = <YCO (as AB II DC, AC transversal , alt. int. angles)
<AXO = <CYO (as AB II DC, XY transversal, alt. int. angles)
Therefore by ASA congruecy,
ΔAXO ≡ ΔCYO
Thus,
AO = CO (CPCT)
XO = YO (CPCT)
So, AC and XY bisect each other.
Hence Proved.

Answer 2

hope this helped u...