Class 7 Maths Part 1 Chapter 7 A Tale of Three Intersecting Lines is the triangle construction chapter. These class 7 maths handwritten notes chapter 7 A Tale of Three Intersecting Lines follow the 2026-27 NCERT and cover equilateral triangles, constructions and altitudes.
- Construction steps written out: each construction given as numbered compass and ruler steps
- What the notes cover: the parts of a triangle, constructing from given sides, altitudes and types of triangles
- Best for: the construction question, which is graded on the steps you show
You can read the complete class 7 maths handwritten notes for A Tale of Three Intersecting Lines, with boxed definitions and quick recall points, in the PDF below.
These handwritten notes are written by Maths teachers, mapped to the 2026-27 NCERT Ganita Prakash book, and checked against Class 7 school question papers.
How Collegedunia's Handwritten Notes Help You Revise A Tale of Three Intersecting Lines
Collegedunia writes its class 7 maths handwritten notes as one clean pass through the chapter. Every construction is written as numbered steps beside the drawing it produces.
- Numbered steps: each construction given as ruler and compass steps in order
- Finished figures: the completed triangle drawn beside its steps, arcs kept
- Type chart: triangles sorted by side and by angle in one grid
- Colour-coded sub-headings: sub-topics in red so each construction is easy to reach
What the A Tale of Three Intersecting Lines Handwritten Notes Cover
A triangle is the most basic closed shape: three vertices and three sides. The chapter builds every construction from that starting point.
- Vertices and sides of a triangle
- Naming a triangle from its vertices
- Equilateral triangles
- Constructing a triangle when all three sides are given
- Constructing when some sides and angles are given
- When a triangle cannot be constructed
- Altitudes of a triangle
- Constructing an altitude
- Types of triangles by sides and by angles
A Tale of Three Intersecting Lines Topic-wise Weightage for CBSE Class 7 Maths
Constructions carry the most marks, and the steps are marked as well as the figure.
| Sub-topic | Weightage | How often asked |
|---|---|---|
| Constructing a triangle from three sides | High | asked often |
| Types of triangles by sides and angles | High | asked often |
| Altitudes and their construction | Medium | asked sometimes |
| When a triangle cannot be constructed | Medium | asked sometimes |
| Equilateral triangle properties | Medium | asked sometimes |
| Naming triangles from vertices | Low | asked rarely |
Why A Tale of Three Intersecting Lines Is Worth Revising Carefully
Construction marks are the most predictable in the geometry section, because the steps are always the same.
- A construction question appears in every geometry test
- Arcs left on the page earn method marks
- Types of triangles is a straight one-mark question
- Part 2 Chapter 1 on congruence continues from these constructions
Last 24-Hour Revision Card for A Tale of Three Intersecting Lines
Read this card before you pick up the compass in the exam.
- A triangle has three vertices and three sides
- Equilateral: all three sides equal; isosceles: two equal; scalene: all different
- Two sides together must be longer than the third
- An altitude is the perpendicular from a vertex to the opposite side
- Never rub out your construction arcs
A Tale of Three Intersecting Lines Self-Assessment Quiz
Five triangle questions. Tap each to check.
A triangle with all three sides equal is called
(a) scalene (b) isosceles (c) equilateral (d) right-angled
Answer: (c) equilateral
Can a triangle have sides 2 cm, 3 cm and 6 cm?
(a) yes (b) no, because 2 + 3 is less than 6 (c) yes, if the angles are right (d) only with a protractor
Answer: (b) no, because 2 + 3 is less than 6
The perpendicular from a vertex to the opposite side is the
(a) base (b) median (c) altitude (d) arc
Answer: (c) altitude
A triangle with two equal sides is
(a) equilateral (b) isosceles (c) scalene (d) obtuse
Answer: (b) isosceles
How many vertices does a triangle have?
(a) 2 (b) 3 (c) 4 (d) 6
Answer: (b) 3
Key Terms and Ideas in A Tale of Three Intersecting Lines
Construction answers need the right vocabulary in the step descriptions.
| Term / Idea | What it means |
|---|---|
| Vertex | a corner point of a triangle |
| Side | a line segment joining two vertices |
| Equilateral triangle | a triangle with all three sides equal |
| Isosceles triangle | a triangle with two sides equal |
| Scalene triangle | a triangle with all three sides different |
| Altitude | the perpendicular from a vertex to the opposite side |
| Base | the side to which an altitude is drawn |
| Arc | part of a circle drawn with a compass |
Diagrams Drawn by Hand in the A Tale of Three Intersecting Lines Notes
Constructions are drawings, so the notes show every stage.
| Figure drawn by hand | What it shows |
|---|---|
| Triangle parts | vertices, sides and the naming convention labelled |
| Three-side construction | the compass arcs shown at each stage |
| Altitude construction | the perpendicular from a vertex drawn with its arcs |
| Type chart | equilateral, isosceles and scalene drawn side by side |
| Impossible triangle | three lengths that cannot close, drawn to show why |
How to Use These Handwritten Notes for Maths Revision
Use these class 7 maths handwritten notes in two passes. Practise with a compass, not a pencil sketch. The steps only stick through doing them.
- Construct three triangles from three given sides each
- Check the two-sides rule before starting each construction
- Draw an altitude from each vertex of one triangle
- Before the test, revise the numbered steps and the type chart
Other Maths Resources for A Tale of Three Intersecting Lines
Use the notes with the solved exercises and the Ganita Prakash chapter itself.
Class 7 Maths Handwritten Notes for All Chapters
Ganita Prakash Part 1 has eight chapters and Part 2 has seven. The table below links the class 7 maths handwritten notes for every chapter.
| Chapter | Resource |
|---|---|
| Part 1 Chapter 1 | Large Numbers Around Us Handwritten Notes |
| Part 1 Chapter 2 | Arithmetic Expressions Handwritten Notes |
| Part 1 Chapter 3 | A Peek Beyond the Point Handwritten Notes |
| Part 1 Chapter 4 | Expressions using Letter-Numbers Handwritten Notes |
| Part 1 Chapter 5 | Parallel and Intersecting Lines Handwritten Notes |
| Part 1 Chapter 6 | Number Play Handwritten Notes |
| Part 1 Chapter 7 | A Tale of Three Intersecting Lines Handwritten Notes |
| Part 1 Chapter 8 | Working with Fractions Handwritten Notes |
| Part 2 Chapter 1 | Geometric Twins Handwritten Notes |
| Part 2 Chapter 2 | Operations with Integers Handwritten Notes |
| Part 2 Chapter 3 | Finding Common Ground Handwritten Notes |
| Part 2 Chapter 4 | Another Peek Beyond the Point Handwritten Notes |
| Part 2 Chapter 5 | Connecting the Dots... Handwritten Notes |
| Part 2 Chapter 6 | Constructions and Tilings Handwritten Notes |
| Part 2 Chapter 7 | Finding the Unknown Handwritten Notes |
A Tale of Three Intersecting Lines Class 7 Maths Handwritten Notes FAQs
Ques. Where can I download the A Tale of Three Intersecting Lines Class 7 Handwritten Notes PDF?
Ans. The PDF is on this page, free, in both the normal and the HD version.
Ques. Do the notes give the construction steps?
Ans. Yes. Every construction is written as numbered ruler and compass steps, with the finished figure drawn beside it and the arcs kept in.
Ques. How many pages is the Chapter 7 handwritten notes PDF?
Ans. It runs 20 pages and covers all five sections of the chapter plus a quiz.
Ques. When can a triangle not be constructed from three given sides?
Ans. When the two shorter sides added together are not longer than the longest side. For example 2 cm, 3 cm and 6 cm cannot form a triangle, because 2 plus 3 is less than 6.
Ques. What is an altitude of a triangle?
Ans. The perpendicular drawn from a vertex to the opposite side. Every triangle has three altitudes, one from each vertex.
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