Chapter Notes: Understanding Elementary Shapes

# Understanding Elementary Shapes Class 6 Notes Maths Chapter 5

 Table of contents Introduction to Understanding Elementary Shapes Measuring Line Segment What are Angles? How to measure angles? What are Perpendicular Lines? Classification of Triangles What is a Quadrilateral? What is a Polygon? What are Three-Dimensional (3D) Shapes?

## Introduction to Understanding Elementary Shapes

In our day-to-day life, we come across various shapes like curves, lines, triangles and various shapes.

We organize them into line segments, angles, triangles, polygons, and circles.

## Measuring Line Segment

We know that a line segment is a fixed portion of a line.
Every fixed thing has a possibility that it can be measured. So, this makes it possible to measure a line segment.
The measure of line segment is a “number”. This numerical value is called “length of line segment.
Measurement can be done in various ways.

### 1. Comparison by observation

By just looking at the line segments we can tell which one is longer.

Here we see that line segment AB is longer than CD.

But we can’t tell how much longer so other methods were deduced.

### 2. Comparison by tracing

Here, we have to compare AB and CD.

We will use tracing paper this time.

Trace line segment CD onto the paper and place it over the line segment on AB.

Now, we will be able to decide which is longer. This method depends on the accuracy in tracing the line segment.

But if we want to compare with another line segment you have to trace another line segment.
You cannot trace every time you want to compare.
So, yet another method was used.

### 3. Comparison using ruler and a divider

Place the zero mark of the ruler at A. Read the mark against B. This gives the length of AB.

Suppose the length is 5 cm, we may write,

Length AB = 5 cm or more simply as

AB = 5 cm.

Open the divider.

Place the endpoint of one of its arms at A and the endpoint of the second arm at B.

## What are Angles?

When two rays originate from a common point then the turn between two rays around the common point or vertex is called the angle between the two rays.

The two rays joining to form an angle are called arms of an angle and the point at which two rays meet to form an angle is called the vertex of the angle.

In the above figure, two rays  and  are the arm of an angle which meets at common initial point Q (vertex) and form an ∠PQR.
The measure of the angle PQR is written as ∠PQR but instead of writing this we can simply write it as ∠PQR.

Study the following positions:
You stand facing north.

By a ‘right-angle-turn’ clockwise, you now face east.By another ‘right-angle-turn’ you finally face south.

• The turn from north to east is by a right angle.
• The turn from north to south is by two right angles; it is called a straight angle. (NS is a straight line).
• Turning by two straight angles (or four right angles) in the same direction makes a full turn.
• This one complete turn is called one revolution.
• The angle for one revolution is a complete angle.
• An angle smaller than a right angle is called an acute angle.
• If an angle is larger than a right angle, but less than a straight angle, it is called an obtuse angle.

Question for Chapter Notes: Understanding Elementary Shapes
Try yourself:The angle measure for one complete revolution is

## How to measure angles?

The last example was helpful to compare angles with a right angle. We classified the angles as acute, obtuse or reflex.

It cannot be useful if we have to find which one among the two obtuse angles is greater. So in order to be more precise in comparison, we need to ‘measure’ the angles.

We can do it with a ‘protractor’.

The curved edge is divided into 180 equal parts. Each part is equal to a ‘degree’.

We call our measure, ‘degree measure’.
One complete revolution is divided into 360 equal parts. Each part is a degree.
Let us see how to measure the given angle using protractor.
Example:

Put the protractor over the angle and you will be get the accurate measure of angle.

Here, the measure of angle is 60°.

## What are Perpendicular Lines?

When two lines intersect and the angle between them is a right angle, then the lines are said to be perpendicular.

If a line AB is perpendicular to CD, we write AB ⊥ CD.

## Classification of Triangles

Triangles can be classified on the basis of

1. Sides
2.  Angles

### On the basis of Size

On the basis of side lengths, the triangles are classified into the following types:

• Equilateral Triangle: A triangle is considered to be an equilateral triangle when all three sides have the same length.
• Isosceles triangle: When two sides of a triangle are equal or congruent, then it is called an isosceles triangle.
• Scalene triangle: When none of the sides of a triangle are equal, it is called a scalene triangle.

### On the basis of Angles

On the basis of angles, triangles are classified into the following types:
• Acute Triangle: When all the angles of a triangle are acute, that is, they measure less than 90°, it is called an acute-angled triangle or acute triangle.
• Right Triangle: When one of the angles of a triangle is 90°, it is called a right-angled triangle or right triangle.
• Obtuse Triangle: When one of the angles of a triangle is an obtuse angle, that is, it measures greater than 90°, it is called an obtuse-angled triangle or obtuse triangle.

Question for Chapter Notes: Understanding Elementary Shapes
Try yourself:A triangle having three unequal sides is called a

• A four-sided polygon is a quadrilateral.
• It has 4 sides and 4 angles.

Example: Draw a rough sketch of a quadrilateral PQRS.

Draw its diagonals.

Name them.

Is the meeting point of the diagonals in the interior or exterior of the quadrilateral?

The two diagonals are PR and QS.

Diagonal PR and diagonal QS meet at point T which is in the interior of the quadrilateral PQRS.

## What is a Polygon?

A polygon is a closed figure formed of three or more line segments.

• Polygons are two dimensional.
•  They are bounded by straight lines and the shape is closed.
•  Minimum three line segments are required to make a closed figure, thus a triangle is a polygon with a minimum of three sides.

We may classify polygons according to the number of their sides.

Let us see some of them:

Number of sides: 3
Name of polygon: Triangle
Illustration:

Number of sides: 4

Illustration:

Number of sides: 5

Name of polygon: Pentagon
Illustration:

Number of sides: 6

Name of polygon: Hexagon
Illustration:

And the list goes on,

For 7 sides its heptagon

For 8 sides its octagon

For 9 sides its nonagon

For 10 sides its decagon...

## What are Three-Dimensional (3D) Shapes?

• Shapes that have three dimensions like length, breadth and height or depth are called three-dimensional shapes.
• They are also called Three dimensional Figures(3-D).
• Examples: Cone, Spheres, Cubes, Cylinders etc.

What is the face of any surface?

The flat surfaces of any solid are called faces.

What are edges?

Line segments common to intersecting faces of a polyhedron are known as its edges. Line segments that form the solid are called edges.

What are vertices?

Points of intersection of edges of a polyhedron are known as its vertices. Corners of the solid are its vertices.

Number of faces, edges, vertices of Cube have been shown below.

Number of faces, edges, vertices of Cuboid have been shown below.

Number of faces, edges, vertices of Pyramid have been shown below.

Question for Chapter Notes: Understanding Elementary Shapes
Try yourself:The following shape is of a

The document Understanding Elementary Shapes Class 6 Notes Maths Chapter 5 is a part of the Class 6 Course Mathematics (Maths) Class 6.
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## FAQs on Understanding Elementary Shapes Class 6 Notes Maths Chapter 5

 1. What is the importance of understanding elementary shapes?
Ans. Understanding elementary shapes is important because it provides the foundation for learning more complex geometry concepts. It helps in identifying, classifying, and measuring different shapes, which has practical applications in fields such as architecture, engineering, and design.
 2. How do we measure line segments?
Ans. To measure a line segment, we need to use a ruler or a measuring tape. We place the starting point of the ruler at one end of the line segment and read the length at the other end of the ruler. The length is typically measured in units such as centimeters or inches.
 3. What are perpendicular lines?
Ans. Perpendicular lines are two lines that intersect at a right angle (90 degrees). They form a square corner and are commonly found in geometric shapes such as rectangles and squares. The symbol for perpendicular lines is ⊥.
 4. What are three-dimensional shapes?
Ans. Three-dimensional (3D) shapes are objects that have three dimensions - length, width, and height. Examples of 3D shapes include cubes, spheres, cones, and cylinders. These shapes have volume and can be measured in cubic units such as cubic centimeters (cm³) or cubic inches (in³).
 5. How do we classify triangles?
Ans. Triangles can be classified based on their sides and angles. Based on sides, they can be classified as equilateral (all sides are equal), isosceles (two sides are equal), or scalene (no sides are equal). Based on angles, they can be classified as acute (all angles are less than 90 degrees), obtuse (one angle is greater than 90 degrees), or right (one angle is exactly 90 degrees).

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