NCERT Class 10 Mathematics Mathematics: Chapter 6 — 1 Introduction
This chapter introduces the concept of similar figures in NCERT Class 10 Mathematics. Building upon the understanding of congruent figures from Class IX, it defines similar figures as those having the same shape but not necessarily the same size. The chapter explores examples like circles, squares, and equilateral triangles, establishing that all congruent figures are similar, but the converse is not always true. It highlights that similarity is crucial for indirect measurements, such as calculating the heights of mountains or distances to celestial bodies. The chapter sets the stage for discussing the similarity of triangles and its application in proving the Pythagorean Theorem.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 10 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 6 — 1 Introduction |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 404 |
Learning outcomes
- Define similar figures and differentiate them from congruent figures.
- Understand that figures with the same shape are similar.
- Recognize that all circles, squares, and equilateral triangles are similar.
- Appreciate the role of similarity in indirect measurements.
- Prepare for the study of triangle similarity and the Pythagorean Theorem.
Vocabulary
| Word | Meaning |
|---|---|
| Congruent | Figures having the same shape and the same size. |
| Similar figures | Figures having the same shape but not necessarily the same size. |
| Indirect measurements | Methods used to find distances or heights without direct measurement, based on principles like similarity. |
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Practice questions
- What is the difference between congruent and similar figures? Answer: Congruent figures have the same shape and size, while similar figures have the same shape but not necessarily the same size.
- Are all circles similar? Explain. Answer: Yes, all circles are similar because they all have the same shape, regardless of their radius (size).
- Give an example of figures that are similar but not congruent. Answer: Two circles with different radii are similar but not congruent.
- What is the principle behind finding the height of Mount Everest? Answer: The principle of similarity of figures is used for indirect measurements like finding the height of Mount Everest.
Frequently asked questions
What are similar figures in mathematics?
Similar figures are geometric figures that have the same shape but may have different sizes.
Are all congruent figures similar?
Yes, all congruent figures are similar because they have both the same shape and the same size.
Are all similar figures congruent?
No, similar figures need not be congruent. They can have different sizes.
What is the main idea of this chapter's introduction?
The introduction defines similar figures and distinguishes them from congruent figures, highlighting their importance in indirect measurements.
Can a circle and a square be similar?
No, a circle and a square cannot be similar because they do not have the same shape.
How is similarity used in real life?
Similarity is used in indirect measurements to find distances or heights of objects that cannot be measured directly, like mountains or distant celestial bodies.
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NCERT Class 10 Mathematics — Mathematics — Chapter 6 — 1 Introduction. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.