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ABCD is a parallelogram and line segments AX and CY bisect angles A and C. Show that AX||YC.

Asked by Topperlearning User 4th June 2014, 1:23 PM
Answered by Expert
Answer:

1 = 2, 3 = 4 And A=C

AD=BC

D=B

(by ASA rule)

DX = BY BY = DX

AB = CD

AB - BY = DC - DX

AY = CX

AY||CX

AYCX is a parallelogram

AX||CY

OR,

A = C

(Opposite angles of parallelogram ABCD)

Therefore,

A = C

i.e., YAX = YCX …(1)

Also, AYC + YCX = 180º (Because YA || CX)…. (2)

Therefore, AYC + YAX = 180º [From (1) and (2)]

So, AX || CY (As interior angles on the same side of the transversal are supplementary)

Answered by Expert 4th June 2014, 3:23 PM
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