Trapezium – Definition – Properties

Altitude – Midsegment –  Angles – Formula 

Definition:

A trapezium is a flat closed quadrilateral with 4 straight sides with one pair of parallel sides. The sides can be vertical, horizontal or slanting.
A trapezium is also known as a trapezoid.

The parallel sides is called the base and the non parallel sides are called legs of the trapezium.

Mid Segment 

If in a trapezium midpoints of legs are connected by a line segment then the line segment is called midsegment.  

The length of midsegment is equal to half of the sum of the bases.

In figure, Mid segment = 1/2(AB+CD)  

Angles

Sum of all interior angles is 360 degree.

 ∴ ∠A + ∠B + ∠C + ∠D = 360 degree.

Sum of two interior angles on same side of side of transversal is 180 degree.

                ∴ ∠A + ∠D = 180 degre

               ∴ ∠B + ∠C = 180 degree

Altitude

The perpendicular distance between the parallel sides of trapezium is known as altitude.  

Properties

• The bases of the trapezium are parallel to each other.
• The sum of the interior angles of a trapezium is 360 degree.
• Sum of 2 angles on same side is equal to 180 degree, or two angles on same side are supplementary. 
• If both pairs of opposite sides of a trapezium is parallel then it is a parallelogram.