Class 3 — Mathematics

Geometry: Lines, Shapes and Symmetry

Class 3

✓By the end of this lesson students will be able to identify and draw different types of lines.
✓By the end of this lesson students will be able to recognise and name basic two-dimensional (2D) shapes like square, rectangle, triangle, and circle.
✓By the end of this lesson students will be able to count the number of sides and corners of basic 2D shapes.
✓By the end of this lesson students will be able to understand the concept of symmetry and identify symmetrical figures.
✓By the end of this lesson students will be able to draw a line of symmetry for simple symmetrical shapes.

Key concepts

Lines

A line is a straight or curved path that extends without end in both directions. In Class 3, we learn about different types of lines:\n\n1. **Straight Lines**: These are lines that do not bend.\n * **Horizontal Line**: A straight line that goes from left to right, like the horizon.\n * **Vertical Line**: A straight line that goes from top to bottom, like a standing pillar.\n * **Slanting Line**: A straight line that is neither horizontal nor vertical, it is tilted.\n\n2. **Curved Lines**: These are lines that are not straight; they bend or are round.\n\n3. **Line Segment**: A part of a straight line that has two definite endpoints. It has a fixed length.

Shapes (Two-Dimensional or 2D Shapes)

2D shapes are flat shapes that can be drawn on a piece of paper. They have only length and breadth. We learn about their sides and corners.\n\n1. **Square**: A shape with four straight sides, all of which are equal in length. It has four corners.\n2. **Rectangle**: A shape with four straight sides. Its opposite sides are equal in length. It has four corners.\n3. **Triangle**: A shape with three straight sides and three corners.\n4. **Circle**: A round shape with no straight sides and no corners.

Symmetry (Introduction)

A shape is said to be symmetrical if it can be folded into two identical halves that match exactly. The fold line is called the **line of symmetry**.\n\n* If you can fold a shape along a line and both parts match perfectly, the shape is symmetrical.\n* If the parts do not match, the shape is asymmetrical.

Key facts to remember

1A line segment is a part of a line with two endpoints.
2Straight lines can be horizontal, vertical, or slanting.
3A square has 4 equal sides and 4 corners.
4A rectangle has 4 sides, with opposite sides equal, and 4 corners.
5A triangle has 3 sides and 3 corners.
6A circle is a round shape with no sides and no corners.
7A symmetrical figure can be folded into two identical halves.
8The fold line that divides a symmetrical figure into two identical halves is called the line of symmetry.

Worked examples

Example 1

Identify the types of lines present in the letter 'A'.

IStep 1: Observe the letter 'A'.

IIStep 2: Notice the two lines that go downwards from the top point. These are slanting lines.

IIIStep 3: Notice the line that connects the two slanting lines in the middle. This is a horizontal line.

IVStep 4: Count the total number of slanting lines and horizontal lines.

Answer

The letter 'A' has two slanting lines and one horizontal line.

Many letters and objects around us are made of different types of lines.

Example 2

Count the number of sides and corners for a triangle and a rectangle.

IStep 1: Consider a triangle. Draw or imagine a triangle.

IIStep 2: Count its straight boundary lines. These are the sides. A triangle has 3 sides.

IIIStep 3: Count its meeting points of the sides. These are the corners. A triangle has 3 corners.

IVStep 4: Now, consider a rectangle. Draw or imagine a rectangle.

VStep 5: Count its straight boundary lines. These are the sides. A rectangle has 4 sides.

VIStep 6: Count its meeting points of the sides. These are the corners. A rectangle has 4 corners.

Answer

A triangle has 3 sides and 3 corners. A rectangle has 4 sides and 4 corners.

Always remember that a circle has no sides and no corners.

Example 3

Draw a line of symmetry for a square.

IStep 1: Draw a square.

IIStep 2: Imagine folding the square exactly in half so that both parts match perfectly.

IIIStep 3: You can fold it from top to bottom (vertically). Draw a vertical line through the middle of the square.

IVStep 4: You can also fold it from left to right (horizontally). Draw a horizontal line through the middle of the square.

VStep 5: You can also fold it along its diagonals. Draw lines connecting opposite corners.

Answer

A square has multiple lines of symmetry. You can draw a vertical line through its centre, a horizontal line through its centre, and two diagonal lines connecting opposite corners. Any one of these lines represents a line of symmetry.

Some shapes have only one line of symmetry, while others have many, and some have none.

Common mistakes

✗Confusing horizontal, vertical, and slanting lines.
✗Incorrectly counting the number of sides or corners for shapes, especially for a circle.
✗Thinking that a circle has sides or corners.
✗Drawing a line of symmetry incorrectly, where the two halves do not match exactly.
✗Not understanding that a line segment has a definite length, unlike a line.

Exam tips

★Practice drawing different types of lines neatly using a ruler.
★Memorise the properties (number of sides and corners) of basic 2D shapes like square, rectangle, triangle, and circle.
★For symmetry, try to imagine folding the shape or use tracing paper to check if the halves match perfectly.
★Read the questions carefully to understand whether you need to identify lines, shapes, or lines of symmetry.

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