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Important Formulas: Understanding Quadrilaterals | Mathematics (Maths) Class 8 PDF Download
Polygons
A simple closed curve made up of only line segments is called a polygon.
Convex Polygon
We have all the diagonals inside the Polygon
Concave Polygon
We don’t have all the diagonals inside the Polygon
Regular and Irregular Polygons
A regular polygon is both ‘equiangular’ and ‘equilateral’. So all the sides and angles should be same
(a) So square is a regular polygon but rectangle is not
(b) Equilateral triangle is a regular polygon
Classification of polygons
We classify polygons according to the number of sides (or vertices)
Terms
1. Quadrilateral
A quadrilateral is a four-sided polygon with four angles. There are many kinds of quadrilaterals. The five most common types are the parallelogram, the rectangle, the square, the trapezoid, and the rhombus.
2. Angle Property of Quadrilateral
- Sum of all the interior angles is 360º
- Sum of all the exterior angles is 360º
3. Parallelogram: A quadrilateral which has both pairs of opposite sides parallel is called a parallelogram.
Its properties are:
- The opposite sides of a parallelogram are equal.
- The opposite angles of a parallelogram are equal.
- The diagonals of a parallelogram bisect each other.
- The adjacent angles in a parallelogram are supplementary.
4. Trapezium: A quadrilateral which has one pair of opposite sides parallel is called a trapezium.
5. Kite: It is a quadrilaterals having exactly two distinct consecutive pairs of sides of equal length
Here ABCD is a Kite
AB=BC
AD=CD
6. Rhombus: Rhombus is a parallelogram in which any pair of adjacent sides is equal.
Properties of a rhombus:
- All sides of a rhombus are equal
- The opposite angles of a rhombus are equal
- The diagonals of a rhombus bisect each other at right angles.
7. Rectangles: A parallelogram which has one of its angles a right angle is called a rectangle.
Properties of a rectangle are:
- The opposite sides of a rectangle are equal
- Each angle of a rectangle is a right-angle.
- The diagonals of a rectangle are equal.
- The diagonals of a rectangle bisect each other.
8. Square: A quadrilateral, all of whose sides are equal and all of whose angles are right angles.
Properties of square are:
- All the sides of a square are equal.
- Each of the angles measures 90°.
- The diagonals of a square bisect each other at right angles.
- The diagonals of a square are equal.
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FAQs on Important Formulas: Understanding Quadrilaterals - Mathematics (Maths) Class 8
| 1. What are the properties of different types of quadrilaterals? |  |
Ans. Quadrilaterals are four-sided polygons, and their properties vary based on their types. For example, a rectangle has opposite sides that are equal and all angles measuring 90 degrees. A square, which is a special type of rectangle, has all sides equal and all angles also at 90 degrees. A parallelogram has opposite sides that are equal and parallel, while a trapezoid has at least one pair of parallel sides. Understanding these properties helps in identifying and classifying quadrilaterals.
| 2. How do you calculate the area of a quadrilateral? | |
Ans. The area of a quadrilateral can be calculated using different formulas depending on its type. For a rectangle, the area is found by multiplying the length by the width (Area = length × width). For a parallelogram, the area is calculated as Area = base × height. For a trapezoid, the formula is Area = 1/2 × (base1 + base2) × height. For irregular quadrilaterals, you may divide the shape into triangles or other polygons, calculate their areas, and sum them up.
| 3. What is the sum of the interior angles of a quadrilateral? | |
Ans. The sum of the interior angles of any quadrilateral is always 360 degrees. This can be derived from the formula for the sum of interior angles of a polygon, which is (n-2) × 180 degrees, where n is the number of sides. Since a quadrilateral has four sides, the calculation becomes (4-2) × 180 = 2 × 180 = 360 degrees.
| 4. How do you determine if a quadrilateral is a parallelogram? | |
Ans. To determine if a quadrilateral is a parallelogram, you can use several criteria:
1. If both pairs of opposite sides are equal in length.
2. If both pairs of opposite angles are equal.
3. If the diagonals bisect each other.
4. If one pair of opposite sides is both equal in length and parallel. If any of these conditions are met, the quadrilateral is a parallelogram.
| 5. What are the differences between a rhombus and a rectangle? | |
Ans. The main differences between a rhombus and a rectangle lie in their properties. A rhombus has all four sides of equal length and opposite angles that are equal, but its angles are not necessarily 90 degrees. In contrast, a rectangle has opposite sides that are equal and all angles measuring 90 degrees. While a square is both a rhombus and a rectangle, a rhombus does not have to have right angles, and a rectangle does not have to have all sides equal.
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