CBSE Class 9 Answered
ABCD is a parallelogram and line segments
AX and CY bisect angles A and C. Show that AX||YC.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
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 | 04 Jun, 2014, 03:23: PM
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