Download A Tale of Three Intersecting Lines – NCERT Class 7 Maths Chapter 7 PDF from the new NCERT Class 7 Maths book Ganita Prakash (2026-27). Read the chapter online or download the free PDF. A triangle has three vertices, three sides and three angles. It is named by its vertices in any order — ∆ABC, ∆BAC and ∆CAB are the same triangle.
A Tale of Three Intersecting Lines PDF – Chapter 7 of Ganita Prakash (Part I)
Read the chapter online or download the PDF.
| Chapter | Download | |
|---|---|---|
| Chapter 7 PDF | A Tale of Three Intersecting Lines | View PDF |
| Full book | NCERT Class 7 Maths – Ganita Prakash | View Book |
Read Online
What Is in A Tale of Three Intersecting Lines? (Class 7 Maths Chapter 7)
- A triangle has three vertices, three sides and three angles. It is named by its vertices in any order — ∆ABC, ∆BAC and ∆CAB are the same triangle.
- Two arcs drawn with a compass meet at the third vertex, so a triangle whose three sidelengths are known can be constructed exactly, without trial and error.
- Triangle inequality: a triangle exists for three lengths exactly when each length is less than the sum of the other two. It is enough to test the longest length.
- A triangle can also be built from two sides and the included angle, or from two angles and the included side — the latter only when the two angles add to less than 180°.
- Angle sum property: the three angles of any triangle add up to 180°. The proof draws a line through one vertex parallel to the opposite side.
- An altitude is the perpendicular from a vertex to the opposite side; in an obtuse triangle the base has to be extended to receive it.
- Triangles are classified by sides as equilateral, isosceles and scalene, and by angles as acute-angled, right-angled and obtuse-angled.
Quick revision – A Tale of Three Intersecting Lines
| Idea | What it means | Example from the chapter | Key result |
|---|---|---|---|
| Triangle | Three vertices joined by three sides | ∆ABC | 3 sides, 3 angles |
| Equilateral triangle | All three sides equal | 4, 4, 4 | Each angle 60° |
| Isosceles triangle | Two sides equal | 5, 5, 8 | Two equal angles |
| Scalene triangle | All three sides different | 3, 4, 5 | All angles different |
| Compass construction | Two arcs of the given radii cross at the third vertex | 4 cm, 5 cm, 6 cm | Exact, no trials |
| Triangle inequality | Each length < sum of the other two | 10, 15, 30 → 30 > 10 + 15 | No triangle |
| Shortcut test | Check only the longest length | 4, 5, 8 → 8 < 4 + 5 | Triangle exists |
| Two circles | Sum of the two smaller lengths vs the longest | <, =, > | Only > gives a triangle |
| Two sides + included angle | Side, included angle, side | 5 cm, 45°, 4 cm | Always one triangle (angle < 180°) |
| Two angles + included side | Angle, included side, angle | 45°, 5 cm, 80° | Needs sum of angles < 180° |
| Angle sum property | ∠A + ∠B + ∠C | Line through A parallel to BC | 180° |
| Exterior angle | Angle between an extended side and the other side | ∠A = 50°, ∠B = 60° | ∠ACD = 110° = 50° + 60° |
| Altitude | Perpendicular from a vertex to the opposite side | AD, BE, CF | Height of the triangle |
| Angle-based types | By the largest angle | Acute / right / obtuse | One right or obtuse angle at most |
Old NCERT vs New – Class 7 Maths
This chapter is from Ganita Prakash, the new NCERT Class 7 Maths book (NCF-SE 2023, used from 2025-26). It replaced the old book “Mathematics”, so chapter numbers and names differ from older PDFs.
Solutions and All Chapters
Answers to the exercises and the full chapter list of Ganita Prakash:
A Tale of Three Intersecting Lines – Overview
| Class | Class 7 |
| Subject | Maths |
| Book | Ganita Prakash – new NCERT book |
| Part | Part I |
| Chapter | 7 of 15 – A Tale of Three Intersecting Lines |
| Book pages | 146 – 172 |
| Edition | NCERT Reprint 2026-27 |
| Session | 2026-27 |
| Free – read online or download |
Class 7 Maths Chapter 7 – FAQs
Where can I download A Tale of Three Intersecting Lines Class 7 PDF?
From the download table on this page – the chapter PDF is free, and the full book is linked too.
What is Class 7 Maths Chapter 7 about?
A triangle has three vertices, three sides and three angles. It is named by its vertices in any order — ∆ABC, ∆BAC and ∆CAB are the same triangle.
Is A Tale of Three Intersecting Lines from the new NCERT Class 7 Maths book?
Yes. It is chapter 7 of ganita prakash (part i), the new NCERT Class 7 Maths book for 2026-27.
Is this the latest NCERT edition for 2026-27?
Yes – the PDF is NCERT’s latest edition for the 2026-27 session.
Where are the NCERT Solutions for Class 7 Maths Chapter 7?
Open the NCERT Solutions link above for answers to the exercise questions.