Q. 54.4( 181 Votes )

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

Answer :

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

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