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Example 2 - Prove that an equilateral triangle can be - Examples

Example 2 - Chapter 5 Class 9 Introduction to Euclid's Geometry - Part 2

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Example 2 Prove that an equilateral triangle can be constructed on any given line segment. Equilateral triangle is a triangle with all sides equal. We prove this by geometry. 1. Draw a line segment AB of any length. 2. Take compass, put the pointy end at point A & pencil at point B. 3. Draw an arc. Here we draw an arc of radii AB. 4. Now put the pointy end at B & pencil at A. 5. Draw another arc. Here we draw an arc of radii BA. 6. Mark the intersecting point as C. 7. Join point A to point C by a straight line. 8. Join point B to point C by a straight line. We need to prove AB = AC = BC Now AC = AB (Radii of same circle) & BC = AB (Radii of same circle) From Euclid’s axiom, things which are equal to the same thing are equal. So, AC = BC. So, we get AB = AC = BC , ∴ ∆ABC is an equilateral triangle.

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.