**Quadrilateral**

Any closed figure in plane, bounded by four line segments is called a Quadrilateral. In the given quadrilateral :

i) Four vertices are

ii) Four line segments are

iii) Four angles are

iv) Two diagonals are

Let’s also learn the nomenclature related to quadrilaterals:

1) Adjacent Sides: Two sides of a quadrilateral having a common vertex. Example are adjacent sides with D as the common vertex. Similarly, are adjacent sides with common vertex B.

2) Opposite Sides: Two sides of a quadrilateral that doesn’t share a common vertex. Example: are opposite side. Similarly, are opposite sides. You will also see that they don’t share any common vertex.

3) Adjacent Angles: Two angles of a quadrilateral having a common arm are called adjacent angles Example: In the above figure are adjacent and they share as the common arm. Similarly, are adjacent angles and they share as the common arm.

4) Opposite Angles: Angles in a quadrilateral that doesn’t share any common arm are called opposite angles. Example: In the above figure, are opposite angles. Similarly, are opposite angles.

Important Theorem:

Remember, in Polygons we read

Sum of the interior angles

In a quadrilateral,

Substituting in the above formula, we get that the sum of the internal angles is

Another way of proving this is as follows:

In

Similarly, in

Adding i) and ii) we get

Or

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