Basic Geometrical Ideas Class 6 Maths Formulas

The List of Important Formulas for Class 6 Basic Geometrical Ideas is provided on this page. We have everything covered right from basic to advanced concepts in Basic Geometrical Ideas. Make the most out of the Maths Formulas for Class 6 prepared by subject experts and take your preparation to the next level. Access the Formula Sheet of Basic Geometrical Ideas Class 6 covering numerous concepts and use them to solve your Problems effortlessly.

The term ‘Geometry’ is the English equivalent of the Greak word ‘Geometron’. ‘Geo’ mean 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. In this chapter, we shall learn some interesting facts which enable us to know more about the shapes around us.

Let us mark a dot on the paper by a sharp tip of the pencil. Sharper the tip, thinner will be the dot. This almost invisible thinner dot gives us an idea of a point. A point determines a location. The following are some models for a point.

Points

It is a position or location on a plane surface, which are denoted by a single capital letter.

A Line Segment

A line segment is the shortest join of two points. The line segment joining two points A and B is denoted by \(\bar { AB }\) or \(\bar { BA }\). The points A and B are called the endpoints of the segment.
Note: \(\bar { AB }\) and \(\bar { BA }\) denote the same line segment.

A Line

A line is obtained when a line segment like \(\bar { AB }\) is extended on both sides indefinitely. It is denoted by \(\bar { AB }\). Sometimes it is denoted by a single letter like l. Although a line contains a countless number of points, yet two points are enough to determine a line. We say ‘two points determine a line.’

Intersecting Lines

Two lines are called intersecting lines if they have one common point.

Real Life Examples of Intersecting Lines

Parallel Lines

Two lines in a plane are said to be a parallel line if they do not intersect.

Real Life Examples of Parallel Lines

Ray

A ray is a portion of a line. It starts at one point (called starting point) and goes endlessly in a direction.

Real life examples of ray are:

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 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.

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.

A closed curve has 3 parts which are as follows

1. Interior of the curve

It refers to the inside/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 outside / 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”.

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.

• 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.

Angle

An angle is made up of two rays starting from a common endpoint. Two rays OP and OQ starting from the common endpoint O form ∠POQ (or also called ∠QOP) at O. Point O is called the vertex of ∠POQ. Rays OP and OQ form two sides of ∠POQ. Note that in specifying an angle, the vertex is always written as the middle letter.
An angle leads to three divisions of a region:

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 inside/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 outside / 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

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 \(\bar { AB }\), \(\bar { BC }\) and \(\bar { CA }\). 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 black line is the boundary.
• The interior of the triangle. - Here, the light blue coloured area is the interior of the angle.
• The exterior of the triangle. - Whereas, the dark blue area is the exterior of the angle.

Quadrilateral

A quadrilateral is a four-sided polygon. It has 4 sides and 4 angles. A quadrilateral has 4 vertices which should be named cyclically.

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.

Circle

A circle is a path of a point moving at the same distance from a fixed point. It is a simple closed curve and is not considered as a polygon.

Parts of Circle

Radius – The fixed point is called the center, the fixed distance is called the radius. The fixed point is called the center, the fixed distance is called the radius

Diameter –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.

Circumference – The distance around the circle is called the circumference

Chord - A chord of a circle is a line segment joining any two points on the circumference.

Arc – It is the portion of the boundary of the circle.

Interior of the Circle – Area inside the boundary of the circle is called the Interior of the Circle.

The Exterior of the Circle – Area outside the boundary of the circle is called the Exterior of the Circle.

Sector- It is the region in the interior of a circle enclosed by an arc on one side and a pair of radii on the other two sides.

Segment - It is the region in the interior of the circle enclosed by an arc and a chord.

• On the circle
• The interior of the circle
• The exterior of the circle.

Semi-Circle

A diameter divides the circle into two semi-circles. Hence the semicircle is the half of the circle, which has the diameter as the part of the boundary of the semicircle.