abcd is a parallelogram. x nad y are points on diagonal bd show that dx =by
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In △AXD and △CYB
∠ADX=∠CBY [Alternate interior angle ]
AD=CB [Opposite sides of parallelogram ABCD]
DX=BY [Given]
∴△AXD≅△CYB [Using SAS congruence]
∴AX=CY [By CPCT]
Now,
In △AYB and △CXD
∠ABY=∠CDX [Alternate interior angle ]
AB=CD [Opposite sides of parallelogram ABCD]
DX=BY [Given]
∴△AYB≅△CXD [Using SAS congruence]
∴AY=CX [By CPCT]
From the result we obtained AX=CY and AY=CX
Since opposite sides quadrilateral AXCY are equal to each other
Therefore, AXCY is a parallelogram
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