Properties of Quadrilaterals
Any simple closed Figure is called a quadrilateral, if it is a simple, closed polygon, with four sides, four vertices and four angles
Thus to define a quadrilateral, it is a closed figure formed by joining 4 line segments, which sometimes have all equal sides like square or rhombus, sometimes have all unequal sides called irregular quadrilateral , sometimes have adjacent sides equal as in kite and sometimes have opposite sides equal as in case of rectangles. In a quadrilateral, we can draw figures in different types. Following are the Properties of Quadrilaterals:
1. A quadrilateral is a simple closed curve.
2. Any quadrilateral is formed by joining 4 line segments.
3. All quadrilaterals have 4 vertexes, 4 angles.
4. opposite vertex of all the quadrilaterals join to form the diagonals of the quadrilateral.
5. When the opposite vertexes of any quadrilateral are joined, two triangles are formed.
6. Sum of all four angles of a quadrilateral is 360ᶱ(degrees) as we can observe that it is formed by joining two triangles and the sum of angles of a triangle is 180ᶱ.
The quadrilaterals are of following types:
a) Square: A four sided figure, which has all the four sides equal and all its 4 angles are of 90ᶱ. Its opposite sides are parallel and equal. The diagonals of a square bisect each other at 90 ᶱ. The diagonals of a square are equal and perpendicular to each other.
b) Rectangle: A four sided figure, which has opposite pair of lines equal and all its angles are 90ᶱ. Its opposite sides are also parallel and equal. Its diagonals bisect each other and are equal. But they are not perpendicular to each other.
c) Rhombus: It’s a tilted form of the square, which means that it’s all sides are equal and opposite sides are parallel to each other. In Rhombus we do not have its angles equal to 90ᶱbut they have their diagonals perpendicular to each other. The diagonals of the rhombus are not equal but they are perpendicular bisector to each other.
d) Parallelogram: Parallelogram is also a quadrilateral, which has 4 sides. Its opposite pairs of lines are equal and parallel to each other.
In a parallelogram, we also have opposite pairs of angles equal and the pair of adjacent angles are supplementary, which means that the sum of the adjacent angles of the parallelogram is 180 ᶱ. Also sum of all the angles of the quadrilateral is 360ᶱ . . It does not have any line of symmetry. But special parallelogram ( a square has 4 lines of symmetry and a rectangle has 2 lines of symmetry).
We must remember that a square, rectangle and rhombus are all special types of parallelogram, as in all these figures, we have opposite sides equal and parallel.
Besides them, we have trapezium, kite, and irregular quadrilaterals in the family of quadrilaterals
e) Kite is a special type of a quadrilateral which has adjacent pair of lines as equal. It has one vertical line of symmetry.
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