Question

Prove that equilateral triangle can be constructed on any given line segment.

Answer 1

Take two points A and B. Pass a line through it. Meaure it. Let it be of 6 cm. Open the compass for 6 cm,keep the pointer at A and draw an arc , now keep the pointer at B and draw an arc cutting the previous arc. Let the point of intersection of these two arcs be C. Join AC and BC. Thus a new triangle is formed ABC of 6 cm each i.e. it is an equilateral triangle. Thus an equilateral triangle can be formed on any line segment.( Just measure it and construct it ).

Answer 2

Given - In ∆ABC one side is 5cm
Construction - Draw a ∆ABC using following steps -
1) Draw a line segment AB = 5cm
2) Using compass point A is centre and radius 5cm draw a arc
3) Using compass assume point B is centre and same radius draw a arc.
4) Both arc is cut this point which name is C
5) Thus we draw a equilateral traingle