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

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.

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.

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.

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

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

Example

#### Triangle

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

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

• 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.

• 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.