Maths Shapes and Patterns - CBSE Notes

What are Shapes?

Shapes help us understand the world around us. Everything we see has a shape—whether it's a ball, a book, or a pizza!

• Shapes are the outlines or boundaries of objects.
• They can be made using curves, points, and line segments.
• Some shapes have straight edges, while others are round.
• Examples: Circle, Square, Rectangle, Triangle.

Types of Shapes

1. Open Shapes

Some shapes do not have a complete boundary. They have gaps in between.

• Open shapes are made of line segments or curves that do not connect completely.
• Example: Letter C, Letter U, A curved line.
  

2. Closed Shapes

These shapes have a complete boundary with no gaps.

• A closed shape starts and ends at the same point.
• Example: Letter O, Letter B, Letter D, A triangle, A square.

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Practice Question

Identify the open and the close shapes.

Answer: Figure 1 is open shape rest all figures are of close shape.

Common Shapes and Their Properties

1. Circle

A circle is a round shape that has no corners or straight lines.

• It is a two-dimensional (2D) shape.
• No edges, no corners.
• Examples: Steering wheel, Pizza, Dartboard.
  

2. Oval

An oval looks like a stretched circle.

• It has no straight lines or corners.
• Example: Number 0 (zero), An egg, A balloon.
  
  

3. Square

A square is a shape with four equal sides.

• All four sides are of the same length.
• It has four corners and four edges.
• Examples: Chessboard, Carrom board, Window pane.
  

4. Rectangle

A rectangle looks like a square but has two longer and two shorter sides.

• Opposite sides are equal in length.
• It has four corners and four edges.
• Examples: Laptop screen, Mobile phone screen, Door.

5. Triangle

A triangle has three sides and three corners.

• It can have different side lengths.
• Examples: Nachos, a slice of pizza, a road sign.
  
  

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Counting Triangles

Triangles are often hidden inside bigger shapes. To count them, we follow a simple method:

• Step 1: Look at the shape carefully and find all the small triangles inside.
• Step 2: Number the base of each small triangle.
• Step 3: Add the numbers of the small triangles to find the total.

Let's Practise:

Sam wants to count the number of triangles present in the given image?

Ans: 
Here, Sam wants to count the total number of triangles present in theimage. So, Sam will use the concept of counting shapes to find how many triangles are present:
Step1: Identify the different shapes present in the image. Here, in theabove image, only triangles are present. 
Step2: Add the numbers to the base of the small triangles. Here, we have2 small triangles in the first layer and 2 small triangles in the second layer.

Step3: To calculate the total number of triangles, add base numbers present on each layer.

• Number of triangles in the first layer = 3
• Number of triangles in the second layer = 3
• Total number of triangles in both layers = 3+3 = 6
• So, the total number of triangles present in the image is 6

Parts of a Shape

1. Edges

Edges are the lines that make up a shape.

• Example: A square has 4 edges, a triangle has 3 edges.
  

2. Corners (Vertices)

Corners are the points where two edges meet.

• Example: A rectangle has 4 corners, a triangle has 3 corners.

Edges and Corners in Different Shapes

Patterns and Designs

Shapes can be used to create beautiful patterns.

• Patterns repeat the same shape again and again.
• We can find patterns in floor tiles, weaving, and nature.
• Examples of patterns:
  • Floor designs
  • Wall decorations
  • Tiling patterns

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Practice Questions

1: Identifying Shapes

Look at the shapes below and answer the following questions:

Which of these shapes is an open shape?

(a) Triangle
(b) Letter C 
(c) Square
(d) Circle

  View Answer

2. Which of these shapes has no edges and no corners?
(a) Rectangle
(b) Oval 
(c) Square
(d) Triangle

  View Answer

3. How many corners does a square have?
(a) 2
(b) 3
(c) 4
(d) 5

  View Answer