Question

AX and CY are respectively the bisectors of opposite angles A and C of a parallelogram ABCD . Show that AX is parallel to CY

Answer 1

Ello There!

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Question: AX and CY are respectively the bisectors of opposite angles A and C of a parallelogram ABCD . Show that AX is parallel to CY

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Answer

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)

$\frac{1}{2}$ ∠A = $\frac{1}{2}$∠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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Thank You!