Q: 8    If the non-parallel sides of a trapezium are equal, prove that it is cyclic.

Given: ABCD is a trapezium.

AB || DE    (Given )

AD || BE    ( By construction )

Thus, ABED is a parallelogram.

AD = BE     (Opposite sides of parallelogram )

so,  BE = BC

In EBC,

BE = BC    (Proved above )

Thus, ...........1(angles opposite to equal sides )

...............2(Opposite angles of the parallelogram )

From 1 and 2, we get

(linear pair)

Thus, ABED is a cyclic quadrilateral.

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