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A quadrilateral is a simple closed geometric figure with four sides and four angles. In simple words, a quadrilateral has four points lying in the same plane, out of which no three are collinear, and those points are joined by lines that do not intersect each other except at their common endpoints. A quadrilateral has 4 angles, 2 pairs of opposite sides and 4 pairs of adjacent sides each and a pair of diagonals.
Contents
Quadrilateral Examples:
Square, Rectangle, Kite, Rhombus, Parallelogram and Trapezium are examples of the quadrilateral.
A Rectangle
A Square
A Parallelogram
What are the Vertices of a Quadrilateral?
The common point joining the sides of a quadrilateral is said to be the vertices of a quadrilateral.
Quadrilateral
In quadrilateral ABCD, shown in the above figure, A, B, C and D are the vertices.
What are the edges of a quadrilateral?
The line segments joining the vertices of the quadrilateral are said to be the edges or sides of that quadrilateral.
In the quadrilateral ABCD shown above, AB, BC, AD and CD are the edges.
How many Diagonals does a Quadrilateral Have?
Let us see how many diagonals does quadrilateral have. The line segments joining the non-adjacent opposite vertices of a quadrilateral are called the diagonals of a quadrilateral. The diagonals of a quadrilateral intersect and bisect each other.
Number of Diagonals in Quadrilateral
In quadrilateral ABCD shown above, AC and BD are the diagonals.
How many Angles are there in a Quadrilateral?
Let us see how many angles does a quadrilateral have? Angles of a quadrilateral refer to the angles formed at each vertex by the adjacent sides of the quadrilateral. A quadrilateral has 4 angles. The sum of a quadrilateral’s angles is [360^circ ].
In quadrilateral ABCD shown above, [angle {rm{A}}],[angle {rm{B}}],[angle {rm{C}}] and [angle {rm{D}}] are the angles of the quadrilateral.
Adjacent Sides of a quadrilateral
The sides of a quadrilateral with a common endpoint are called its adjacent sides.
Quadrilateral ABCD
In the given figure, (AB, BC), (BC, CD), (CD, DA) and (DA, AB) are four pairs of adjacent sides of quadrilateral ABCD.
Solved Examples :
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Identify the pairs of adjacent sides from the given figure.
Solution: In the given quadrilateral, WXYZ, (WX, XY), (XY, YZ), (YZ, ZW) and (ZW, WX) are the pairs of adjacent sides.
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Identify the pairs of adjacent sides from the given figure.
Solution: In the given quadrilateral PQRS, (PQ, QR), (QR, RS), (RS, SP) and (SP, PQ) are the pairs of adjacent sides.
Conclusion:
Thus, a quadrilateral is a closed figure with 4 vertices, 4 sides, 4 angles and 2 diagonals. A quadrilateral has 4 pairs of adjacent sides and 2 pairs of opposite sides. Talking about the angles, it has 2 pairs of opposite angles and 4 pairs of adjacent angles. Examples of quadrilaterals are Square, Rectangle, Rhombus, Parallelogram, Kite and Trapezium.
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