If the non-parallel sides of a trapezium are equal, prove that it is cyclic.
Solution:
It is given that ABCD is a trapezium with
and
We need to prove that ABCD is a cyclic quadrilateral.
Construction: Draw
and
.
In
and
, we have
(Given)
(Each equal to
)
(Distance between two parallel lines is constant.)
Therefore, by RHS congruence rule, we have
(Corresponding parts of congruent triangles are equal) (1)
We also have
(Co-interior angles,
) (2)
From (1) and (2), we can say that
ABCD is a cyclic quadrilateral.
(If the sum of a pair of opposite angles of a quadrilateral is
, the quadrilateral is cyclic.)
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