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Subjects /Class 6 / Mathematics.6 / Basic Geometrical Ideas

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INTRODUCTION
25 Aug 2021

Geometry has a long and rich history. The term ‘Geometry’ is the English equivalent of the greek word ‘Geometron’.

The meaning of geometry includes:

  • Geo means Earth
  • metron means Measurement.

Therefore, geometry refers a branch of Mathematics that studies the sizes, shapes, positions angles and dimensions of things.

It is used to calculate the area or capacity related to any shape.

Line Segment

Joining two points A and B is denoted by \(\overline{\mathrm{AB}}\) or \(\overline{\mathrm{BA}}\).


The points A and B are called the endpoints of the segment.


Intersecting lines

The two lines that share one common point.

This shared point is called the point of intersection.


Here, line l and m are intersecting at point C.

Parallel Lines

Two or more lines that never intersect or Never cross each other are called Parallel Lines.


Ray

It is a part of a line with one starting point whereas extends endlessly in one direction.


Curves

Anything which is not straight is called a curve.

1. Simple Curve:

A curve that does not cross itself.


2. Open Curve:

Curve in which its endpoints do not meet.

3. Closed Curve:

Curve that does not have an endpoint and is an enclosed figure.

Closed Curve

Parts of Curve

A closed curve has 3 parts which are as follows:

1. Interior

2. Exterior

3. Boundary

 

1. Interior of the curve

  • It refers to the inner area of the curve.
  • The blue coloured area is the interior of the figure.

2. The exterior of the curve.

  • It refers to the outer area of the curve.
  • The point marked A depicts the exterior of the curve.

3. The boundary of the curve

  • It refers to the dividing line thus it divides the interior and exterior of the curve.
  • The black line which is dividing the interior and exterior of the curve is the boundary.
  • The interior and boundary of the curve together are called the curves “region”.


Polygon

A closed curve made up entirely of line segments.

It is a 2d closed shape made of line segments / straight lines only.

Polygons

Parts of a Polygon

Sides

  • It refers to the line segments which form the polygon, as in the above figure AB, BC, CD, DA are its sides.

Vertex

  • Point where 2 line segments meet, as in the above figure A, B, C and D are its vertices.

Adjacent Sides

  • If any 2 sides share a common endpoint they are said to be adjacent to each other thus called adjacent sides.
  • As in the above figure AB and BC, BC and CD, CD and DA, DA and AB are adjacent sides.

Adjacent Vertices

  • It refers to the endpoints of the same side of the polygon.
  • As in the above figure A and B, B and C, C and D, D and A are adjacent vertices.

Diagonals

  • It refers to the joins of the vertices which are not adjacent to each other.
  • As in the above figure, AC and BD are diagonals of the polygon.

Angles

  • It’s made up of two rays starting from a common endpoint.

Angles

It’s made up of two rays starting from a common endpoint.

A Below Figure formed from 2 rays which share a common endpoint.

Angles

The rays forming the angle are known as its arms or sides.

The common endpoint is known as its vertex.

An angle is also associated with 3 parts:

  1. Interior -
    • It refers to the inner area.
    • The green coloured area is the interior of the angle.
  2. Angle/boundary -
    • It refers to the arms of the angle.
    • The red point is on the arm of the angle.
  3. Exterior -
    • It refers to the outer area.
    • The blue point depicts the exterior of the figure.

Naming an Angle:


While naming an angle the letter depicting the vertex appears in the middle.

Example

Angle

  • The above angle can also be named as CBA.
  • An angle can also be named just by its vertex.

Example

Angle

Triangle

It is a 3-sided polygon. It is also the polygon with the least number of the sides.

Triangle

  • Vertices: A, B and C
  • Sides: AB, BC and CA
  • Angles: A, B and C

Triangle

  • Here, the light blue coloured area is the interior of the angle.
  • The black line is the boundary.
  • Whereas, the dark blue area is the exterior of the angle.

Quadilaterals

  • It’s a 4-sided polygon.

Quadrilaterals

  • Vertices: A, B, C, D
  • Sides: AB, BC, CD, DA
  • Angle: A, B, C, D
  • Opposite Sides: AB and DC, BC and AD
  • Opposite Angles: B and D, A and C
  • Adjacent Angles: A and B, B and C, C and D, D and A.