**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:**

Exercise | Topics |

4.1 | Basic Geometrical Shapes |

4.2 | Curves |

4.3 | Angles |

4.4 | Triangles |

4.5 | Quadrilaterals |

4.6 | Circle |

**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**

Terms | Definition |

Point | It determines a location and is usually determined by a capital letter. |

Line segment | The shortest distance between two points is called a line segment. |

Line | By extending a line segment indefinitely on both sides, a line is obtained. |

Intersecting lines | If two distinct lines meet or cross at a point, they are called intersecting lines. |

Parallel lines | Parallel lines are lines which are always the same distance apart and never intersect anywhere in a plane. |

Ray | A ray is a line which starts from a particular point and goes infinitely towards a particular direction. |

Curve | It is a drawing which is done without lifting the pencil. |

Simple curve | A curve that never crosses itself is a simple curve. |

Closed and open curves | A curve is closed if its ends are joined. Otherwise, it is an open curve. |

Angle | It is made up of two rays which are starting from a common point. |

**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 Notes | CBSE Class 6 Maths Study Notes |

Knowing our Numbers Class 6 Notes Chapter 1 | Decimals Class 6 Notes Chapter 8 |

Whole Numbers Class 6 Notes Chapter 2 | Data Handling Class 6 Notes Chapter 9 |

Playing with Numbers Class 6 Notes Chapter 3 | Mensuration Class 6 Notes Chapter 10 |

Basic Geometrical Ideas Class 6 Notes Chapter 4 | Algebra Class 6 Notes Chapter 11 |

Understanding Elementary Shapes Class 6 Notes Chapter 5 | Ratio And Proportion Class 6 Notes Chapter 12 |

Integers Class 6 Notes Chapter 6 | Symmetry Class 6 Notes Chapter 13 |

Fractions Class 6 Notes Chapter 7 | Practical Geometry Class 6 Notes Chapter 14 |

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