The Surajkund Fair Chapter Notes | Mathematics for Class 3 (Maths Mela) PDF Download

Introduction

Understanding Symmetry

• Symmetry in refers to shapes that are exactly alike when moved, rotated, or flipped.
  Example: When cutting out a heart shape from paper, folding the paper in half allows one to draw and cut out one-half, resulting in a symmetrical heart shape.

• Symmetry is often described as a mirror image where an object looks identical after being turned or flipped.
• It is present in patterns and denotes balance and proportionate similarity between two halves of an object.
• Objects lacking symmetry are termed asymmetrical.

Symmetrical Figures

• Symmetrical shapes or figures are those where a line can be placed or drawn such that the images on both sides of the line, mirror each other.
  Examples of symmetrical figures include squares, circles, triangles, and hearts.
  
• Dotted lines in the figures given below show the line of symmetry:
  
• Drawing lines of symmetry helps identify symmetrical properties in shapes.
  Example: Figure (b) exhibits symmetrical figures when two lines of symmetry are drawn.
  
• Study the following images:
  The dotted lines in the figures given above are not lines of symmetry. If the figure is cut along the dotted line, then both the parts when folded along the dotted line do not fit exactly into each other. 

Mirror Images

• When we place an object in front of a mirror, we see its reflection, which is called a mirror image.
• In a mirror image, the right side of the object looks like the left side, and the left side looks like the right side. This is called lateral inversion.
• Combining an object and its mirror image creates symmetry, where both sides look the same.
  Mirror Images of Capital Letters
• Certain letters and numbers have mirror images that look exactly like their original forms.
  Mirror Images of Small letters Mirror Images of Numbers 
• For example, letters like A, H, M, and numbers like 0 and 8 have mirror images that are the same as their original forms.

Understanding mirror images helps us notice how things change when we look at them in a mirror!

What is Geometry?

Whenever we look near to us, we see different objects of different shapes and sizes. Also, different figures hold different similarities. However, the question is how to find out which figure is what.

Geometry is all about shapes and how they work. Geometry is a branch of mathematics that deals with the study of shapes, sizes, properties of space, and the relationships between points, lines, angles, surfaces, and solids.

Point

A tiny dot ‘·’ represents a point. We name points by a capital letter such as A, B, C,  D, ... which we write near the dot.

A point shows an exact location or position. It has no length, breadth or depth.

Line Segment

• The figure shows three paths from a fixed point A to another fixed point B. Two paths are curved and one path is straight. The straight path is the shortest path. 
• We call the straight path between the fixed points A as B a line segment.
• A line segment AB has two end points, A and B and is denoted by drawing a bar over AB, i.e., You can draw a line segment through two points A and B with the help of a ruler.
• Put a ruler in such a way that one of its straight edges touches both the points. Now, move the pencil from A to B along the edge of the ruler.
• Whenever two line segments meet, they meet at a point.

Edurev Tips: A line segment has a fixed length.

Observe the following figures:
In the first figure, line segments CD and AB are meeting at the point A. In the second figure, line segments CD and AB are meeting at the point P. In the third figure, line segments AB and BC are meeting at the point B.

We use line segments to build figures as given below:

Line

A line is different from a line segment. A line does not have a beginning or an end. The picture of a line is drawn by putting arrowheads at both ends. The arrowheads at ends tell us that it goes on and on in both directions.
The figure given below shows the line AB. It is denoted as:

• A line segment is a part of a line.
• A line has no end points and it has no fixed length.

Ray

A ray is a part of a line which can be extended endlessly in one direction only.

Think of the rays of the Sun. Do they have a starting place and then go on and on in one direction?

• A ray has only one end-point which is its tailpoint.
• To name a ray, first name its end-point. Then, name any other point on the ray.
• Thus, the ray having end point P and Q as any other point on it is denoted by

Look at the following figures:
What is the end point of ray PQ?
Ans: P
Of ray QP?
Ans: Q
Why is  not the same as  
Ans: Their directions and end-points are different.

Measuring the Length of a Line Segment

To measure the length of a line segment, a ruler is used.

• To measure the length of a line segment say  first, place the edge of the ruler showing the centimetres along the line segment AB. 
• Remember to adjust ‘0’ on the ruler at point A. Read the mark on the ruler at the other point B of the given line segment.
• Here, the point B is at the 8 cm mark on the ruler. So, the length of the given line segment is 8 cm.

To Draw a Line Segment of Given Length

Method

Suppose, we have to draw a line segment of length 6 cm.

Step 1: Place the ruler on the plane paper and hold it as shown in the figure.
Step 2: Mark two points A and B against the marks 0 and 6 on the ruler.
Step 3: Pressing the ruler evenly, join these two points A and B with a pencil. The line segment AB thus drawn is the required line segment 6 cm long.

If instead of joining the points against the marks 0 and 6, you had joined them against the marks 1 and 7, or 2 and 8 or 5 and 11 etc., you would have still drawn a line segment 6 cm long.

Line Segments having same Length

• Look at the line segments given below.
  
• Can you tell without measuring whether the line segment AB is longer than, shorter than or of the same length as the line segment CD? (Ans: No)
• Trace the line segments AB and CD.
• You can open your compasses, as shown for the line segment AB above. Place the steel tip at one end point and the pencil tip at the other end point. 
• Now, place the steel tip on point C. Without changing the opening of the compasses, if the pencil tip can be made to touch point D, then the line segments have the same length.

Edurev Tips: We will indicate the fact that measures of AB and CD are equal by writing AB = CD and for the sake of simplicity read that AB is equal to CD.

Plane Shapes

As, you can draw them on a sheet of paper or a plane surface, they are called plane shapes or plane figures.

1. Rectangle

The figure given on the right is a rectangle. It has four corners (vertices) and four sides.
If you measure its sides, you will find that:

Opposite sides of a rectangle are equal.

In the rectangle ABCD, we have:
Vertices: A, B, C, D;
Sides: AB, BC, CD, DA;
Diagonals: AC and BD

The line segment joining the opposite vertices of the rectangle is called its diagonal.

As can be seen from the figure, a rectangle has two diagonals. If you measure them, you will observe that the diagonals of a rectangle are of equal length. 
Thus, AC = BD.

The corner of a plane figure is called a vertex. The plural of ‘vertex’ is ‘vertices’.

2. Square

A square is a closed figure. It has four sides and four vertices. If you measure its sides, you will find that:

All the sides of a square are equal.

In the square PQRS, we have: 
Vertices: P, Q, R, S;
Sides: PQ, QR, RS, SP;
Diagonals: PR and SQ
A square also has two diagonals, which are of equal length
Thus, in a square PQRS, we haveand diagonal

3. Triangle

The figure shown alongside is of a triangle. It has three vertices and three sides. In the triangle XYZ, we have:
Vertices: X, Y, Z;
Sides: XY, YZ, ZX
The sides of a triangle may or may not be equal.

4. Circle

A circle is a simple closed curve. It does not have any corner or side.
Look at the figure given alongside:
Will the bullock move along a circular path, if the rope is tight.
Ans: Yes
If several stones are placed along the path, will the distance from the stake to each of these points be the same? 
Ans: Yes

5. Parts of a Circle

A circle has a centre. A line segment from the centre to the circle is called radius.
Point O is the centre. OA is a radius.

Drawing a circle

Compasses are used to draw circles. The pictures given below show how to do it.

• Mark some point to be the centre of the circle.
• Name this point A. Use a ruler to locate a point that is 4 cm from point A in any direction you choose. Call this point B.
• Put the steel tip of the compasses as on A. Open or close the compasses so that the pencil tip is on B. Press down on the steel tip and turn the compasses to draw a circle. This circle has a 4 cm radius.

Idea of Space

1. The football rolls on the ground. Where does it go after rising off from the ground when it is kicked up? It moves up in space.
   
2. Have you heard or seen a pilot bailing out from his aeroplane in an emergency? He does so with the help of a parachute.
   The aeroplane moves in space. The paratrooper moves in space after having bailed out.
   
3. Have you ever seen a satellite? It moves in space. The moon also moves in space. All the stars move in space. Our earth also moves in space.
   
4. You walk on the ground. You swim along the length and breadth of a swimming pool. When you jump from the diving board, you move in space.
   

Solids

Can you draw a tennis ball, a match box, an icecream, a die, a drum, etc. on a plain sheet of paper?
Ans: No
At the most you can represent a football by a circle. Such bodies are called solids.
They are 3-dimensional objects and not flat like plane figures. Solid shapes have length, width and depth.

A solid occupies a fixed amount of space.

Some common solid shapes are shown below:

Plane and Curved Surfaces

A solid occupies space. The part of a solid which we usually see and touch is called the surface of the solid. Solids have different types of surfaces.
The notebook and the blackboard have plane surfaces. The ball and the globe have curved surfaces.
Some objects like an unsharpened pencil (cylinder) have both types of surfaces.

Faces, Edges and Vertices

• A face is a flat surface of a solid figure.
• An edge is formed where two or more two faces meet.
• A corner of a solid is called a vertex. It is a point where the two or more edges meet.

More about Solid Shapes

1. Cube

• A cube has 6 plane faces, 12 edges and 8 vertices.
• All the six faces are identical. They are squares.
• Common examples of a cube are: Ice cube, Playing die, Rubik’s cube, etc.

2. Cuboid

• A cuboid has 6 plane faces, which are rectangles, 12 edges and 8 vertices. Its opposite faces are identical.
• Common examples of a cuboid are: Matchbox, Book, Gift box, etc.

3. Cylinder

• A cylinder has 2 plane faces and 1 curved face. 
• It has 2 edges and no vertices.
• Common examples of a cylinders are: Paint can, Post box, Soft drink can, etc.

4. Cone

• A cone has 1 plane face and 1 curved face. 
• It has 1 edge and 1 vertex. 
• Common examples of a cone are: Icecream cone, Joker’s cap, Traffic cone, etc.

5. Sphere

• A sphere has only 1 curved face. 
• It has no vertices and no edges. 
• Common examples of a sphere are: Orange, Football, Earth, etc.