In the adjoining figure, ABCD is a parallelogram and line segments AX and CY bisect `angle A and angle C ` respectively. Proove that AX||CY.

Explanation

We have : ` angle A = angle C " " ("opp. " angle " of a|| gm")`
`rArr (1)/(2) angle A = (1)/(2) angle C rArr angle 1 = angle 2. " " `…(i)
Now, DC||AB and CY is a transversal
`rArr angle 2 =angle 3 " " ...(ii) ("alt. interion "angle )`.
From (i) and (ii), we get `angle 1 = angle 3.`
But, these are corresponding angles formed when AX and CY are cut by transversal AB.
` therefore ` AX ||CY.