ABCD is a parallelogram and line segments AX, CY bisect the ∠ A and ∠C, respectively. Show that AX||CY.

To Prove: AX||CY

Given: ABCD is a parallelogram and line segments AX, CY bisect the angles A and C.

Concept Used:

Diagram:

Explanation:

Now from the figure, we can see that,

AB || CD

And as AX is the bisector of ∠A, we get,

∠A = ∠C [Opposite angles of a parallelogram are equal]

1/2 ∠A = 1/2 ∠C

Therefore,

∠1 = ∠2

Now,

∠ 2 = ∠3 [AB||CD, and CY is a transversal to both]

Now, we can say that,

∠1 = ∠3

And this forms a corresponding angles pair.

Thus, we can say that AX || CY.

Hence, Proved.