Question

Prove that an equilateral triangle can be constructed on any given line segment.<br />

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

on the line let (AB) take the measure of line using compass and then draw 60 degrees on A using compass and extend the line . NOW DRAW ANOTHER 60 DEGREES ON B USING COMPASS AND EXTEND THAT LINE . THE POINT WHERE BOTH THE LINES MEET
NAME THAT POINT C
ABC IS THE Required equilateral triangle