CBSE Class 6 Maths Notes Chapter 4 Basic Geometrical Ideas

Introduction to Basic Geometrical Ideas

In this chapter, several important geometric terms.The topics that are introduced not only will help students to build a foundation in geometry but will also help them to grasp the higher-level concepts in the later grades easily.Basic Geometrical Ideas Class 6 Notes Maths Chapter 4

The main topics covered here are-

  • Basic Definitions in Geometry
  • Polygons
  • Triangles
  • Quadrilaterals
  • About Circles

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The different topics covered in CBSE Class 6 Mathematics Chapter 4 are tabulated below:

ExerciseTopics
4.1Basic Geometrical Shapes
4.2Curves
4.3Angles
4.4Triangles
4.5Quadrilaterals
4.6Circle

Exercise 4.1 –  Basic Geometrical Shapes

  • The term ‘Geometry’ is the English equivalent of the Greak word ‘Geometron’.
  • ‘Geo’ means Earth and ‘metron’ Means Measurement.
  • Geometrical ideas are reflected in fill forms of art, measurements, architecture, engineering, etc.
  • We observe and use different objects.
  • These objects have different shapes.
  • The ruler is straight whereas a ball is round.

Basic Definitions in Geometry

TermsDefinition
PointIt determines a location and is usually determined by a capital letter.
Line segmentThe shortest distance between two points is called a line segment.
LineBy extending a line segment indefinitely on both sides, a line is obtained.
Intersecting linesIf two distinct lines meet or cross at a point, they are called intersecting lines.
Parallel linesParallel lines are lines which are always the same distance apart and never intersect anywhere in a plane.
RayA ray is a line which starts from a particular point and goes infinitely towards a particular direction.
CurveIt is a drawing which is done without lifting the pencil.
Simple curveA curve that never crosses itself is a simple curve.
Closed and open curvesA curve is closed if its ends are joined. Otherwise, it is an open curve.
AngleIt is made up of two rays which are starting from a common point.
Basic Geometrical Ideas Class 6 Notes Maths Chapter 4

Exercise 4.2 –  Curves

  • Any drawing (straight or non-straight) drawn without lifting the pencil from the paper and without the use of a ruler is called a curve.
  • In everyday use the curve means ‘not straight’ but in mathematics, a curve can be a straight line also.
  • A curve is called a simple curve if it does not cross itself.
  • A curve is said to be a closed curve if its ends are joined; otherwise, it is said to be open.
  • In a closed curve, there are three disjoint parts:
  • Interior
  • Boundary
  • Exterior
  • The interior of a curve together with its boundary is called its region.
  • In simple terms, any line that is not straight is said to be a curve.
  • If a curve does not cross itself, then it is called a simple curve.

Exercise 4.3 –  Angles

  • An angle is made by two rays starting at a common endpoint.
  • These rays are called the arms of the angle.
  • The common endpoint is called the vertex of the angle.
  • While naming an angle the vertex of the angle has to be in the middle.
  • For example: Ray OP and Ray OQ form an angle. It can be denoted as ∠POQ.
  • Ray OP and OQ are the arms or sides of the angle. O is the vertex of the angle POQ

Exercise 4.4 –  Triangles

  • A triangle is a three-sided polygon.
  • Actually, it is a polygon with the least number of sides.
  • Triangle ABC is written as ∆ABC. There are three sides of a triangle.
  • Thus, sides of ∆ABC are , (overline {AB} ,overline {BC} ) and (overline {CA} ) .. There are three angles in a triangle.
  • Thus, angles of ∆ABC are ∠BAC, ∠ABC, and ∠BCA.
  • The points A, B, and C are called the vertices of the triangle ABC.
  • Like angle, a triangle also has three regions associated with it.
  • On the triangle
  • The interior of the triangle
  • The exterior of the triangle.

Exercise 4.5 –  Quadrilaterals

A quadrilateral is defined as a four-sided polygon i.e. having 4 line segments or sides and thus, 4 angles. A diagram of a quadrilateral is given for better understanding. It should be noted that the vertices of a quadrilateral are named in a cyclic manner.

In this diagram, AD and DC are one of the examples of adjacent sides. Also, AD and BC are one of the opposite sides. Here, angle A and angle C are opposite angles. In this, if the line segment is drawn from A to C or from B to D, it becomes a diagonal.

Exercise 4.6 –  Circle

  • A circle is a path of a point moving at the same distance from a fixed point.
  • The fixed point is called the center, the fixed distance is called the radius and the distance around the circle is called the circumference.
  • A chord of a circle is a line segment joining any two points on the circumference.
  • A diameter is a chord passing through the center.
  • A diameter is double the size of a radius.
  • Any diameter of a circle divides it into two semi-circles.
  • Any portion of a circle is called an arc.
  • For two points P and Q on the circle, we get the arc PQ denoted PQ(vector)
  • Like a simple closed curve, there are three regions associated with a circle.
  • On the circle
  • The interior of the circle
  • The exterior of the circle.

Polygons

  • A polygon is a closed curve made up entirely of line segments.
  • The line segments forming a polygon are called its sides.
  • The meeting point of a pair of sides is called its vertex.
  • Any two sides with a common endpoint are called the adjacent sides.
  • The endpoints of the same side are called the adjacent vertices.
  • The join of any two non-adjacent vertices is called a diagonal of the polygon.

CBSE Notes for Class 6 Maths Free Download for All Chapters

CBSE Class 6 Maths Study NotesCBSE Class 6 Maths Study Notes
Knowing our Numbers Class 6 Notes Chapter 1Decimals Class 6 Notes Chapter 8
Whole Numbers Class 6 Notes Chapter 2Data Handling Class 6 Notes Chapter 9
Playing with Numbers Class 6 Notes Chapter 3Mensuration  Class 6 Notes Chapter 10
Basic Geometrical Ideas Class 6 Notes Chapter 4Algebra Class 6 Notes Chapter 11
Understanding Elementary Shapes Class 6 Notes Chapter 5Ratio And Proportion Class 6 Notes Chapter 12
Integers Class 6 Notes Chapter 6Symmetry Class 6 Notes Chapter 13
Fractions Class 6 Notes Chapter 7Practical Geometry Class 6 Notes Chapter 14

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