A Tale of Three Intersecting Lines

About this chapter

A Tale of Three Intersecting Lines is Chapter 7 of Class 7 Ganita Prakash. It treats a triangle as the closed figure born when three line segments meet at three corner points. The chapter develops the basic anatomy — three vertices, three sides, three angles, named after the vertices in any order. It then builds, step by step, the conditions under which a triangle can exist and how it is constructed. With a compass the equilateral triangle of any side length is constructed using two intersecting arcs; the same idea extends to triangles of three given sides. Out of this construction grows the triangle inequality — the sum of any two sides must be greater than the third. The chapter then takes up constructions when two sides and the included angle are given, and when two angles and the included side are given, leading naturally to the famous angle sum property: the three angles of every triangle add up to 180°. Exterior angle, altitude (height of a vertex from the opposite side) and the classification of triangles into equilateral, isosceles, scalene and into acute, right, obtuse angled close the chapter. CTET Paper 2 Mathematics tests this chapter through triangle inequality numerics, finding a missing angle using the angle sum property, identifying the type of a triangle from its sides or angles, and exterior-angle relations. The four tests below cover these ideas at the right depth.