Q: 8 If the non-parallel sides of a trapezium are equal, prove that it is cyclic.
Given: ABCD is a trapezium.
Construction: Draw AD || BE.
Proof: In quadrilateral ABED,
AB || DE (Given )
AD || BE ( By construction )
Thus, ABED is a parallelogram.
AD = BE (Opposite sides of parallelogram )
AD = BC (Given )
so, BE = BC
BE = BC (Proved above )
Thus, ...........1(angles opposite to equal sides )
...............2(Opposite angles of the parallelogram )
From 1 and 2, we get
Thus, ABED is a cyclic quadrilateral.