---
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id: "69f86961293c3123114d8f0f"
title: "Triangles"
board: "CBSE"
curriculum: "CBSE"
class: "Class 10"
subject: "Mathematics"
book: "Mathematics"
chapter: "Triangles"
chapter_slug: "triangles"
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source: "Edzy"
version: 1
last_updated: "2026-06-20"
---

# Triangles
In this chapter, we shall study figures that have the same shape but not necessarily the same size, specifically focusing on the similarity of triangles and the indirect measurement principles based on this concept.

---

## Knowledge Snapshot
| Field | Details |
| :--- | :--- |
| Class | Class 10 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Triangles |
| Pages | 73-98 |

---

## Chapter Summary
### Short Summary
This chapter discusses the properties of triangles, focusing on the concept of similarity and the criteria that determine whether two triangles are similar.

### Detailed Summary
We begin with an introduction to triangles and their properties, recalling that two figures are congruent if they have the same shape and size. The chapter elaborates on the concept of similar figures and specific properties of triangles. Key theorems are provided which include the Basic Proportionality Theorem, criteria for similarity (AAA, AA, SSS, SAS), and their applications through examples. Finally, a summary of important points related to triangle properties and similarity is presented.

---

## Topic-Wise Explanation
### Introduction
This section provides a brief overview of triangles and their properties that are foundational to understanding similarity.

### Similar Figures
This topic explains that two figures are similar if they have the same shape but not necessarily the same size, emphasizing examples like circles and equilateral triangles.

### Similarity of Triangles
Here, we discuss the similarity conditions for triangles, stating that they are similar if their corresponding angles are equal and their sides are in the same ratio.

### Criteria for Similarity of Triangles
This section outlines various theorems and criteria (AAA, AA, SSS, SAS) that help determine if two triangles are similar, including the proofs and applications of these criteria.

### Summary
The conclusion summarizes the key findings of the chapter, reiterating the critical properties and theorems regarding triangles and similarity.

---

## Core Ideas
| Idea | Explanation |
| :--- | :--- |
| Similar Figures | Figures that have the same shape but not the same size. |
| Basic Proportionality Theorem | A line drawn parallel to one side of a triangle divides the other two sides proportionally. |
| AAA Criterion | If corresponding angles of two triangles are equal, then their sides are in the same ratio, establishing similarity. |
| AA Criterion | If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. |
| SSS Criterion | If the sides of two triangles are in the same ratio, then the corresponding angles are equal, establishing similarity. |
| SAS Criterion | If one angle of a triangle is equal to one angle of another triangle, and the sides including these angles are proportional, then the triangles are similar. |

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## Important Points for Revision
* Two figures having the same shape but not necessarily the same size are called similar figures.
* All congruent figures are similar, but similar figures need not be congruent.
* To determine similarity in polygons, corresponding angles must be equal, and corresponding sides must be in the same ratio.
* The Basic Proportionality Theorem states that a line drawn parallel to one side of a triangle divides the other two sides in the same ratio.
* The AAA similarity criterion establishes similarity based solely on equal corresponding angles.
* The SSS and SAS criteria provide conditions involving the ratios of corresponding sides for establishing triangle similarity.

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## Practice Questions
### Short Answer Questions
1. Define similar figures with an example.
2. Explain the Basic Proportionality Theorem.
3. What criteria can be used to identify similar triangles?
4. How does the SSS similarity criterion differ from the AAA criterion?
5. Provide an example of a real-world application of triangle similarity.

### Long Answer Questions
1. Prove that if two triangles have two corresponding angles equal, then the triangles are similar.
2. Discuss the significance of the AAA criterion with an example.
3. Elaborate on how the Basic Proportionality Theorem can be applied in real-world measurements.

---

## Related Concepts
* Congruence of Triangles
* Properties of Polygons
* Indirect Measurements

---

## Source Attribution
| Field | Value |
| :--- | :--- |
| Source | Edzy |
| Reference Type | examSubjectBookChapter |
| Reference ID | 69f86961293c3123114d8f0f |
| Canonical URL | https://www.edzy.ai/cbse-class-10-mathematics-triangles |
| Markdown URL | https://www.edzy.ai/okf/chapter/cbse-class-10-mathematics-triangles.md |