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**.

**
**