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CBSE Class 6 Mathematics Chapter 5 Revision Notes – Understanding Elementary Shapes
All the things around us have basic geometrical shapes. They can be either simple line segments or curves or different types of angles or any combination of these. To recognise the basic figures, students must have conceptual clarity about them. Class 6 Mathematics Chapter 5 Notes introduce students to elementary shapes to help them have a better understanding of geometrical figures. When students understand the concepts, they can perform better in the exam hall and obtain high scores. This is the sole objective of Extramarks. These notes aim for clarifying all doubts related to the concepts from the students’ minds and for them to have solid preparation before the exam.
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Access Class 6 Mathematics Chapter 5 – Understanding Elementary Shapes
Understanding Elementary Shapes Notes
Understanding Elementary Shapes Introduction
What is the shape of an object with four edges? Or what is the shape formed by the needles of the clock when it is three o’clock in the morning? What are threedimensional shapes? These questions can be easily answered with a basic knowledge of elementary shapes. Class 6 Mathematics Chapter 5 Notes comprise the following topics to help the students recognise basic shapes in daily life.
 Line segment
 Perpendicular lines and perpendicular bisector
 Angles
 Triangles
 Quadrangles
 Some polygons
 Faces, edges, and vertices
Line Segment
 A line segment is a part of a line having two endpoints on a fixed plane.
 The distance between the two endpoints is called the length of the line segment.
 The length can be measured in various ways. For example, it can be measured with the help of tracing paper or by simple observation. But these are faulty methods. Only a graduated or a scaled ruler and a divider can give an accurate measurement.
Perpendicular Lines and Perpendicular Bisector
 When a line segment intersects another line segment, and the angle formed between them is ninety degrees or a right angle, then it can be said that one line segment is perpendicular to another.
 The prefix “bi” means “two” and sector means divider. In geometry, therefore, a bisector is a line segment that divides another line segment into two equal halves.
 Therefore, a perpendicular bisector is a line segment that is perpendicular to another line segment and divides it into two equal halves.
Angles
 When the needles of a clock shift their location from one place to another they form angles.
 There are many different types of angles, namely,
 right angle
 straight angle
 reflex angle
 complete angle
 acute angle
 obtuse angle
 Right Angle: When a line segment is perpendicular to another line segment it forms a ninetydegree angle. It is called a right angle.
 For example, when the clock strikes three, the angle formed by the two needles is called a right angle.
 Straight Angle: The straight angle is an angle formed by a straight line.
 When it is six o’clock or quarter past nine or five to five, the needles of the clock come in a straight line and form a straight angle.
 The measurement of this angle is 180⁰ or two right angles.
 Reflex Angle: A reflex angle is any angle that is greater than a straight angle but less than a complete angle.
 When it is a quarter past seven by the clock the angle formed on the upper side of the needles is called a reflex angle.
 It is greater than two right angles but lesser than four right angles.
 Complete Angle: A complete angle is formed when the clock strikes twelve. In other words, when a line segment reaches its initial position after completing a full rotation it forms a complete angle.
 The measurement of a complete angle is 360⁰ or four right angles.
 Acute Angle and Obtuse Angle: These angles are named taking the right angle as a reference.
 An angle that is lesser in measurement than a right angle is called an acute angle. An example of the acute angle is the angle formed between the needles when it is ten past twelve.
 An obtuse angle is greater than a right angle but lesser than a straight angle. When the longer needle is at five’s place and the smaller needle is at twelve’s place the angle formed between them is an obtuse angle.
 The instrument that is used to measure the angle is called a protractor.
Triangles
 A triangle is a geometric shape formed by three edges.
 The three edges form three angles at the three vertices.
 Triangles are categorized into the following groups.
 Based on the length of the edges
 Based on the measurement of the angles
 Based on the length of the edges, triangles are further categorized into the following.
 Equilateral triangle
 Isosceles triangle
 Scalene triangle
 Based on the measurement of the angles, there are three types of triangles.
 Acuteangled triangle
 Obtuseangled triangle
 Rightangled triangle
 Definitions of different types of triangles:
 Equilateral triangles: An equilateral triangle is a triangle which has three sides of the same length. If the length of one side of an equilateral triangle is three centimetres then the other sides must be three centimetres.
 Isosceles triangle: An isosceles triangle is a triangle with two sides of equal length. If the length of an edge is five centimetres then one of the two other sides must be the length of five centimetres.
 Scalene triangle: The sides of a scalene triangle are unequal in length. For example: if the length of the sides of a triangle is three centimetres, six centimetres, and seven centimetres, it must be a scalene triangle.
 Acuteangled triangle: As the name suggests, the angles of this kind of triangle are acute angles. In other words, the measurements of angles are less than ninety degrees. If a triangle has three angles of sixty degrees it is an instance of an acute triangle.
 Obtuseangled triangle: The condition of an obtuse triangle is that one angle of the triangle must be an obtuse angle. If any one angle of a triangle is 120⁰ that is definitely an obtuse triangle. There is no need to measure the other angles to reach the conclusion.
 Rightangled triangle: In this type of triangle one angle must be at ninety degrees. For example: if the top point of a light post and the endpoint of its shadow on the street are joined with an imaginary line, it forms a rightangled triangle provided that the light post stands straight on the ground. The right angle is formed at the vertex between the light post and its shadow.
Quadrangles
 Quadrangles are closed geometric shapes formed by four edges.
 The line segment joining the opposite vertices is known as the diagonal.
 Quadrangles can be classified into different categories based on the length of their sides. They are listed below.
 Trapezium
 Parallelogram
 Rectangle
 Rhombus
 Square
 Trapezium
 A trapezium is a quadrilateral with one pair of parallel lines.
 It has all four sides of dissimilar lengths.
 All the angles have different measurements.
 The diagonals also do not bear any similarity.
 Parallelogram
 It is a polygon with four sides that has two pairs of parallel lines.
 Rectangle
 A rectangle is a parallelogram that has four right angles.
 The opposite sides of a rectangle are of the same length.
 The diagonals of a rectangle are equal in length, but they are not perpendicular to each other.
 Rhombus
 It is also a type of parallelogram, but it has all the edges of the same length.
 The diagonals of a rhombus are perpendicular to each other and bisect the angles at the vertices.
 Square
 It has two pairs of parallel sides. So, it is another type of parallelogram.
 All the edges have the same length. So, it is a kind of rhombus.
 It has four right angles like a rectangle.
 All the diagonals of a rectangle are equal in length and perpendicular to each other.
Some Polygons
 Polygons are geometric shapes with many edges.
 Polygons are named based on the number of edges they have.
 Polygons having three sides are called triangles.
 Polygons that have four sides are known as quadrilaterals.
 Polygons with five edges—pentagon.
 Six edges—hexagons.
 Seven edges—heptagon.
 Eight edges—octagon.
 Nine edges—nonagon.
 Ten edges—decagon.
Faces, Edges, and Vertices
 The shapes so far discussed are twodimensional shapes. But there are threedimensional shapes too. Cubes, cuboids, cylinders, cones, spheres, prisms, pyramids, etc., are some of them.
 The flat surfaces of the aforementioned shapes are called faces.
 The line segments of every face are called the edges. Two line segments meet at one edge.
 The meeting point of three edges, or the corner point, is called a vertex.
 A prism with a triangular face is called a triangular prism whereas a prism, with a rectangular face, is known as a rectangular prism.
Benefits of Understanding Elementary Shapes Notes by Extramarks
Extramarks is an online platform where students can easily access highquality notes prepared by professionals. Class 6 Mathematics Chapter 5 Notes prepared by experts at Extramarks help students to have conceptual clarity on elementary shapes so that they can solve any type of question in the exam hall. Experts have taken special care of including all the important points given in the NCERT text so that students can answer all the questions by going through the notes. The topics are explained with suitable examples, which makes it easy for the students to visualize the figures. The FAQs section will further help the students to evaluate their progress after going through the study material. With these notes, students can not only revise the whole chapter in less time but cover every topic effectively.
FAQs (Frequently Asked Questions)
1. What are the basic directions?
The basic directions are north, south, east, and west.
2. The long needle of a clock has moved from the place of twelve to the place of six. The short needle is at the position of three. How many right angles has the long needle formed?
The long needle has formed two right angles in the course of a half revolution.
3. The big hand of the clock is facing south. Now it has turned towards the west. How many right angles has it formed?
The big hand has formed one right angle.
4. A lotus is blooming on the pond. What kind of angle has the stalk of the lotus formed with the surface of the water?
The angle between the stalk and the water surface is ninety degrees. Therefore, it is at a right angle.