In parallelogram ABCD, AX is bisector of angleA
and CY is the bisector of angleC. Prove that AXCY
is a parallelogram.
Answers
Answered by
123
Given,
ABCD is a Parallelogram
AX is the bisector of ∠A
CY is the bisector of ∠C
To Prove
AX ║ CY
Proof
ABCD is a parallelogram
∴ ∠A = ∠C(Opp. angles of a paralleogram are equal)
∠A = ∠C (Halves of equals are equal)
∴ ∠1 = ∠2
(AX and CY bisects A and C)
AB ║CD and CY is the transversal (Parallel lines of a parallelogram)
∴ ∠2 = ∠3
But ∠1 = ∠2
⇒ ∠1 = ∠3
∴ AX ║ CY
(Corresponding angles 1 and 3 are equal, therfore the lines are parallel)
_______________________
Answered by
69
Given,
- ABCD is a Parallelogram
- AX is the bisector of ∠A
- CY is the bisector of ∠C
To Prove
- AX ║ CY
Proof
- ABCD is a parallelogram
∴ ∠A = ∠C(Opp. angles of a paralleogram are equal)
∠A = ∠C (Halves of equals are equal)
∴ ∠1 = ∠2
(AX and CY bisects A and C)
AB ║CD and CY is the transversal (Parallel lines of a parallelogram)
∴ ∠2 = ∠3
But ∠1 = ∠2
⇒ ∠1 = ∠3
∴ AX ║ CY
(Corresponding angles 1 and 3 are equal, therfore the lines are parallel)
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