Question

ABCD is a parallelogram and the segment AX and CY bisect angle A and angle C respectively prove that AX parallel to CY

Answer 1

I have attached the answer . Mark it brainiest please.....

Answer 2

Ello there!

Since opposite angles are equal in a parallelogram. Therefore, in parallelogram ABCD, we have

∠A = ∠C

=> 1/2∠A = 1/2∠C

=> ∠1 = ∠2 [Since AX and CY are the bisectors of ∠A and ∠C respectively] ....(1)

Now, AB || DC and transversal CY intersects them.

Hence, ∠2 = ∠3 [Alternate interior angles are equal] .... (2)

From (1) and (2), we get

∠1 = ∠3

Thus, transversal AB intersects AX and YC at A and Y such that ∠1 = ∠3 i.e., corresponding angles are equal.

Hence, AX || CY ______[ANSWER]