NCERT Class 7 Mathematics Ganita Prakash: Chapter 7 — A Tale of Three Intersecting Lines
This chapter introduces the fundamental concept of a triangle in mathematics, defining its components: vertices and sides. It explains how triangles are named and how their angles are denoted. The chapter then focuses on equilateral triangles, characterized by having all sides of equal length. It delves into the construction of an equilateral triangle, discussing the use of tools like a ruler and compass. The text highlights the efficiency gained by using a compass to draw arcs of a specific radius from the vertices, ensuring all sides meet the required length for equilateral triangle construction. This foundational understanding of triangles and their properties is crucial for further study in geometry.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 7 |
| Subject | Mathematics |
| Book | Ganita Prakash |
| Chapter | Chapter 7 — A Tale of Three Intersecting Lines |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 435 |
Learning outcomes
- Understand the definition and components of a triangle (vertices, sides, angles).
- Learn how triangles are named and their angles are denoted.
- Identify and understand the properties of equilateral triangles.
- Learn the process of constructing an equilateral triangle using a compass and ruler.
- Appreciate the efficiency of using geometric tools for construction.
Vocabulary
| Word | Meaning |
|---|---|
| Vertex | A corner point of a triangle. |
| Side | A line segment forming part of the boundary of a triangle. |
| Angle | The figure formed by two rays sharing a common endpoint (the vertex). |
| Equilateral Triangle | A triangle in which all three sides are of equal length. |
| Compass | A tool used for drawing circles or arcs and for measuring distances. |
| Ruler | A straight edge used for measuring lengths or drawing straight lines. |
| Arc | A portion of the circumference of a circle or of a curve. |
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Practice questions
- What are the three basic components of a triangle? Answer: Vertices, sides, and angles.
- What defines an equilateral triangle? Answer: All three sides are of equal length.
- Which tool is efficient for constructing an equilateral triangle with specific side lengths? Answer: A compass.
- If a triangle has sides of length 5 cm, 5 cm, and 5 cm, what type of triangle is it? Answer: An equilateral triangle.
Frequently asked questions
What is a triangle?
A triangle is the most basic closed shape consisting of three corner points (vertices) and three line segments (sides) that join pairs of vertices.
What are the angles of a triangle?
The three angles are formed where the sides meet at the corners (vertices).
What is special about equilateral triangles?
Equilateral triangles are the most symmetric and have all sides of equal lengths.
Can an equilateral triangle be constructed using only a ruler?
It is possible but might require several trials. Using a compass makes the construction more efficient.
How does a compass help in constructing an equilateral triangle?
A compass is used to draw arcs of a specific radius (equal to the desired side length) from the vertices, ensuring that the third vertex lies at the correct distance from the other two.
What is the minimum number of sides an equilateral triangle has?
An equilateral triangle has exactly three sides.
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Topics covered
NCERT Class 7 Mathematics — Ganita Prakash — Chapter 7 — A Tale of Three Intersecting Lines. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.