**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)**