1.

In the figure AX & CY are respectively the bisectors of the opposite angles A & C of a parallelogram ABCD. Show that AX || CY

Answer»

ANSWER:

∠A = ∠C (Opposite angles of parallelogram ABCD)

Therefore, 1/2 ∠A = 1/2 ∠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)


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