Class 7 Maths Ch 7: A Tale of Three Intersecting Lines – learn to construct and analyse triangles, use triangle inequality, angle sum and exterior angle properties, and draw altitudes, with clear notes, solved examples and quiz for CBSE Exam

Complete Chapter 7 guide: basics of triangles (sides, vertices, angles, naming), constructing equilateral and general triangles using ruler and compass, when a triangle is possible or impossible (triangle inequality with tent–tree–pole story), finding the third angle using a parallel line and proving angle sum property ∠A+∠B+∠C=180°, exterior angles equal to the sum of two interior opposite angles, and altitudes/heights of a triangle with paper‑folding and set‑square constructions, plus solved examples and practice for CBSE Class 7 Maths

Updated: 6 months ago

Categories: Class 7 Mathematics, NCERT Maths Notes 2025, Geometry – Triangles, Constructions & Angle Properties, CBSE Exam Preparation, Practice Questions & Quizzes
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Class 7 Mathematics Chapter 7: A Tale of Three Intersecting Lines – Complete Notes, Solutions, Questions & Answers 2025

A Tale of Three Intersecting Lines

Class 7 Mathematics Chapter 7 | Complete Guide | Triangles, Constructions, Inequality, Angles, Altitudes 2025

Chapter at a Glance – A Tale of Three Intersecting Lines

This chapter introduces triangles, their constructions using compass and ruler, triangle inequality for existence, angle sum property, exterior angles, altitudes, and classification based on sides and angles.

Main Topics Covered

  • Definition of triangles: vertices, sides, angles
  • Equilateral triangles and construction
  • SSS construction
  • Triangle inequality
  • SAS and ASA constructions
  • Angle sum property (180°)
  • Exterior angles
  • Altitudes using set square
  • Types: equilateral, isosceles, scalene; acute, right, obtuse

Key Takeaways for Exams

Triangle Inequality

Each side < sum of other two

Angle Sum

∠A + ∠B + ∠C = 180°

Exterior Angle

Equal to sum of opposite interior angles

Altitude

Perpendicular from vertex to opposite side

Right Triangle

One 90° angle

Equilateral

All sides equal, all angles 60°

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