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Question
ABCD is a parallelogram. The bisector of angle A intersects CD at X and bisector of angle C intersects AB at Y. Is AXCY a parallelogram? Give reason.
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Solution
Given, ABCD is a parallelogram,
So, ∠A = ∠C ...[∵ Opposite angles of a parallelogram are equal]
∴ `(∠A)/2 = (∠C)/2` ...[Dividing both the sides by 2]
∠1 = ∠2 ...[Alternative angles]
But ∠2 = ∠3 ...[∵ AB || CD and CY is the transerval]
∴ ∠1 = ∠3
But they are pair of corresponding angles.
∴ AX || YC ...(i)
AY || XC [∵ AB || DC] ...(ii)
From equations (i) and (ii), we get
AXCY is a parallelogram.
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