Concept of trapezium — lesson. Mathematics CBSE, Class 8.

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A quadrilateral with one pair of parallel side is called trapezium.

Now we are going to define a trapezium

$ABCD$ as a quadrilateral having exactly one pair of parallel sides.

Therefore, if

$ABCD$ is a trapezium in that

$AD$ is parallel to

$BC$ (

$AD||BC$ ).

Here

$∠A + ∠B = 180°$ and

$∠C + ∠D = 180°$ . This condition is because

$AD || BC$ and considering the line

$AB$ as transversal, the angles

$∠A$ and

$∠B$ are alternate interior and alternate exterior angles. Thus, they form a linear pair.

This implies, the angles

$∠A$ and

$∠B$ are supplementary.

Similar way, if we consider the

$CD$ as transversal, the angles

$∠C$ and

$∠D$ are supplementary.

Important!

Terms used in trapezium:

The pair of parallel sides are called the bases while the non-parallel sides are called the legs of the trapezoid.
The line segment connecting the midpoints of the non-parallel sides of a trapezoid is called the mid-segment.
If we draw a line segment, between the two non-parallel sides, from the mid-point of both sides, the trapezium will be divided into two unequal parts.

In a trapezium, the following properties are true:

The sum of all the four angles of the trapezium is equal to $360°$ .
A trapezium has $4$ unequal sides.
A trapezium has two parallel sides and two non-parallel sides.
The diagonals of trapezium bisect each other.
The length of the mid-segment is equal to $\frac{1}{2}$ the sum of the parallel bases, in a trapezium.
Sum of adjacent angles on non-parallel sides of trapezium is $180°$ .

A trapezium is isosceles trapezium, if its non-parallel sides are equal.

Thus, a quadrilateral

$ABCD$ is an isosceles trapezium, if

$AD || BC$ and

$AB = CD$ .