Equilateral Triangles

Class 7 Maths · Chapter 7: A Tale of Three Intersecting Lines · NCERT Ganita Prakash section 7.1

Learn

A triangle has three corner points (vertices) and three sides joining them. We name it by its vertices, in any order: △ABC, △BCA … Its angles are ∠A, ∠B and ∠C. If the three points lie on one straight line, there is no triangle at all.

An equilateral triangle has all three sides equal. To make one with side 4 cm, Kabir draws AB = 4 cm. With only a ruler, he would keep guessing where C goes. Better: C must be 4 cm from A and 4 cm from B.

With a compass: draw an arc of radius 4 cm from A: every point on it is 4 cm from A. Draw an arc of radius 4 cm from B. The point where the arcs cross is 4 cm from both: that is C. Join AC and BC.

AC = 4 cm (arc from A) · BC = 4 cm (arc from B)

The same idea works for any point that must be at given distances from two points. A triangle with two equal sides is isosceles: for AC = BC = 5 cm, draw arcs of 5 cm from both A and B. Points on two equal circles and their centres make many isosceles and equilateral triangles.

Explore: find the third vertex.

1. Mark C so that AC = BC = 5 cm (draw circles of 5 cm around A and B first).

Remember

• Equilateral: all three sides equal; isosceles: two sides equal.
• A point at given distances from A and B is where the two arcs cross.

Quick check

Why is the crossing point of the two 4 cm arcs the third vertex of the equilateral triangle?

1. it is 4 cm from both A and B
2. it is halfway between A and B
3. it is above the base
4. arcs always make equilateral triangles

Think about it

How many different points are 4 cm from both A and B, if AB = 4 cm?

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.