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.
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:
Adding i) and ii) we get