# Isosceles Trapezoid

Sub Topics
A trapezoid is a special type of quadrilateral in which one pair of opposite sides are parallel.

In the above trapezium, AB is parallel to DC and AD & BC are non-parallel sides.
It is also called as non isosceles trapezoid, since the non-parallel sides are not of equal lengths.

## Area of Isosceles Trapezoid

In the above trapezoid ABCD, Area of ABCD = Area of $\Delta$ABC + Area of $\Delta$ADC.

= $\frac{1}{2}$ x AB x h + $\frac{1}{2}$ x CD x h

= $\frac{1}{2}$   ( AB + CD ) x h

= $\frac{1}{2}$ x (sum of parallel sides ) x height

## Isosceles Trapezoid Definition

A Trapezoid where two of the non-parallel sides measure equal lengths.

In the above trapezoid ABCD, AB is parallel to CD. The non-parallel sides AD and BC are of equal lengths.
(i.e)  AD = BC.

## Isosceles Trapezoid Properties

1.    Only one pair of opposite sides are parallel. AB // DC.
2.    The other pair of opposite sides are non-parallel BC is not parallel to AD.
3.    (Isosceles trapezoid diagonals) The Diagonals of isosceles trapezoid are equal. (i.e) The diagonals AC = BD.
4.    (Isosceles trapezoid angles) Two pairs of angles of isosceles trapezoid are equal.[ pairs of acute angles and pairs of obtuse angles are equal ]
(i.e) $\angle$A = $\angle$B and $\angle$C = $\angle$D.
5.    Pairs Interior angles on the same side of the non-parallel sides and between the parallel lines are supplementary.[ sum of an acute + obtuse angle = 180° .
6.    The sum of all the interior angles = 360°.