### Theory:

• Quadrilaterals which has two parallel sides are called Trapezium.

• Parallel sides of Trapezium are called its bases.
$$AD$$ and $$BC$$ — bases.

• Sides, which are not parallel, is called lateral sides of Trapezium.
$$AB$$ and $$CD$$ — lateral sides of the Trapezium.

There are a few kinds of Trapezium most often we talk about acute and isosceles Trapezium.
Right Trapezium

Trapezium, which has one lateral side perpendicular to bases, is called a right Trapezium.
Isosceles Trapezium

Trapezium, which has equal lateral sides, is called an isosceles Trapezium.
Properties of Trapezium
•  Angle: The sum of angles in a trapezium-like other quadrilateral is 360°. So in a trapezium ABCD, ∠A+∠B+∠C+∠D =   $360\mathrm{°}$
• Two angles on the same side are supplementary, that is the sum of the angles of two adjacent sides is equal to $180\mathrm{°}$
• Its diagonals bisect with each other.
• The length of the mid-segment is equal to 1/2 the sum of the bases. In the above figure mid-segment= 1/2 (AB+CD)
• In special cases of the isosceles trapezium, legs of the trapezium are congruent to each other. This means that despite being non-parallel, the measurement of both legs is equal.