Construct an equilateral triangle, given its side and justify the construction.

Given to construct an equilateral triangle and justify the construction.

Let us construct an equilateral triangle of 3 cms length on each side.

Steps of construction:

i. Draw a ray AX.

ii. With 3 cms as radius, draw an arc with centre as A. The place where the arc meets the ray AZ is point B.

iii. Now, with B as centre, draw another arc with the same 3 cms radius intersecting the previous arc at C.

iv. Now join AC and BC to get the required construction where ΔABC is an equilateral triangle.

Justification:

As per the above construction,

AB = BC ---- (1)

[as they are the radii of the same arc]

Also

AB = AC ---- (2)

[as they are the radii of the same arc]

From (1) & (2), we have AB = BC= AC