Question

In the adjoining figure ABCD is a parallelogram. Line segments AX and CY bised 2A and 20
respectively. Prove that
ADX =~CBY
AX= CY
AX || CY
AYCX is a parallelogram​

Answer 1

Answer:

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

∠A = ∠C

⇒ 1 / 2 ∠A = 1 / 2 ∠C

⇒ ∠1 = ∠2 ---- i)

[∵ AX and CY are bisectors of ∠A and ∠C respectively]

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

∴ ∠2 and ∠3 ---- ii) [∵ alternate interior angles are equal ]

From (i) and (ii) , we have

∠1 and ∠3

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

∴ AX | | CY .