ABCD is a //gm and line segment AX and CY bisects angles A and C respectively where X is a point on AB. To prove AX // CY

Given, ABCD is a parallelogram.

A = C (Opposite angles of the parallelogram are equal)

1 = ∠2    ...(1)        [AX is bisector of A and CY is bisector of C]

Now, AB || CD and CY is the transversal.

2 = 3    ...(2)    [Alternate interior angles]

From (1) and (2), we get

1 = 3

Transversal AB intersects AX and CY at A and Y respectively such that 1 = 3 i.e., corresponding angles formed are equal.

 AX || CY.

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