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Points to Remember: Understanding Quadrilaterals | Mathematics (Maths) Class 8 PDF Download

Polygon 

A simple closed curve made up of only line segments is called a polygon.

Points to Remember: Understanding Quadrilaterals | Mathematics (Maths) Class 8

Concave polygons 

Concave polygons are those polygons in which at least one interior angle is a reflex angle and it points inwards. They have a minimum of 4 sides 

Points to Remember: Understanding Quadrilaterals | Mathematics (Maths) Class 8

Convex polygons

A polygon is a two-dimensional shape that has a minimum of three sides and angles. A convex polygon is a shape in which all of its vertices point in the outward direction.

Points to Remember: Understanding Quadrilaterals | Mathematics (Maths) Class 8

Regular and irregular polygons

A regular polygon is a two-dimensional shape having all sides of equal length and all interior angles of equal measure.

Points to Remember: Understanding Quadrilaterals | Mathematics (Maths) Class 8

An irregular polygon, also known as non-regular polygon is a shape that does not have all sides of equal length and all angles of equal. 

Points to Remember: Understanding Quadrilaterals | Mathematics (Maths) Class 8

Parallelogram

A quadrilateral with each pair of opposite sides parallel.

  • Opposite sides are equal. 
  • Opposite angles are equal. 
  • Diagonals bisect one another. 

Points to Remember: Understanding Quadrilaterals | Mathematics (Maths) Class 8

Rhombus

A parallelogram with sides of equal length. 

  • All the properties of a parallelogram. 
  • Diagonals are perpendicular to each other. 

Points to Remember: Understanding Quadrilaterals | Mathematics (Maths) Class 8

Rectangle

A parallelogram with a right angle. 

  • All the properties of a parallelogram. 
  • Each of the angles is a right angle. 
  • Diagonals are equal. 

Points to Remember: Understanding Quadrilaterals | Mathematics (Maths) Class 8

Square

  • A rectangle with sides of equal length. 
  • All the properties of a parallelogram, rhombus, and a rectangle.

Points to Remember: Understanding Quadrilaterals | Mathematics (Maths) Class 8

Kite

A quadrilateral with exactly two pairs of equal consecutive sides.

  • The diagonals are perpendicular to one another.
  • One of the diagonals bisects the other.
  • From figure, m∠B=m∠D  but m∠A≠m∠C

Points to Remember: Understanding Quadrilaterals | Mathematics (Maths) Class 8

Trapezium

A quadrilateral having exactly one pair of parallel sides.
Points to Remember: Understanding Quadrilaterals | Mathematics (Maths) Class 8

Diagonal

  • A simple closed curve is made up of only line segments. 
  • A line segment connecting two non-consecutive vertices of a polygon is called diagonal.

Points to Remember: Understanding Quadrilaterals | Mathematics (Maths) Class 8

Convex: The measure of each angle is less than 180º .
Concave: The measure of at least one angle is more than 180º.
Quadrilateral: A polygon having four sides. 

Element of quadrilateral: 
(i) Sides: Line segments joining the points.
(ii) Vertices: Point of intersection of two consecutive sides.
(iii) Opposite sides: Two sides of a quadrilateral having no common endpoint.
(iv) Opposite Angles: Two angles of a quadrilateral not having a common arm.
(v) Diagonals: A line segment is obtained by joining the opposite vertices.
(vi) Adjacent Angles: Two angles of a quadrilateral having a common arm.
(vii) Adjacent Sides: Two sides of a quadrilateral having a common endpoint.

The document Points to Remember: Understanding Quadrilaterals | Mathematics (Maths) Class 8 is a part of the Class 8 Course Mathematics (Maths) Class 8.
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FAQs on Points to Remember: Understanding Quadrilaterals - Mathematics (Maths) Class 8

1. What are the different types of quadrilaterals?
Ans. The different types of quadrilaterals are parallelogram, rectangle, square, rhombus, trapezium, and kite.
2. How do you identify a quadrilateral?
Ans. A quadrilateral is a polygon with four sides and four angles. It can be identified by counting the number of sides and angles in a shape.
3. What is the sum of the interior angles of a quadrilateral?
Ans. The sum of the interior angles of a quadrilateral is always 360 degrees.
4. How do you classify a quadrilateral based on its sides and angles?
Ans. A quadrilateral can be classified as regular or irregular based on its sides and angles. Regular quadrilaterals have equal sides and angles, while irregular quadrilaterals have different sides and angles.
5. Can a quadrilateral have all right angles?
Ans. Yes, a quadrilateral with all right angles is called a rectangle.
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