Question

9. In parallelogram ABCD, AX is bisector of ZA
and CY is the bisector of ZC. Prove that AXCY
is a parallelogram.
D
С
X
А
B
ABCD is a parallelo-gram​

Answer 1

$\huge\underline\pink{ANSWER:}$

Given,

ABCD is a Parallelogram

AX is the bisector of ZA

CY is the bisector of C

To Prove :

AX ll CY

Proof :

ABCD is a parallelogram

:. ZA = ZC(Opp. angles of a paralleogram are equal)

ZA = ZC (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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