AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see Figure). Show that
and
.
Solution:
Construction: Join AC and BD.
It is given that CD is the longest side and AB is the shortest side in quadrilateral ABCD.
In
and
and
(Given)
and
(In any triangle, the angle opposite to the longer side is larger)
Similarly, In
and
and
(Given)
and
(In any triangle, the angle opposite to the longer side is larger)
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