Question

Prove that an equilateral triangle can be constructed on any given lione segment.​

Answer 1

Answer:

In order to prove the above statement, follow the given steps:-

Step-1- Draw a line segment AB of any length.

Step-2- Taking A as a centre and radius = length of AB, draw an arc above the line segment AB.

Step-3- Now, taking B as a centre and the same radius, draw an arc intersecting the previous arc at the point C.

Step-4- Join AC and CB.

Step-5- ABC is the required equilateral triangle.

This construction proves that an equilateral triangle can be constructed on any line segment.

Answer 2

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 ).