Question

Construct an equilateral triangle, given its side of length of 4.5 cm and justify the construction.

Answer 1

Hint: An equilateral triangle whose all the three sides are equal and all the angles are of ${60^\circ}$. We will first draw a line segment AB of length 4.5 cm.

Complete step-by-step answer:
Now, to draw an equilateral triangle, we have to follow the steps given below:
1. We will first draw a line segment AB of length 4.5 cm.

2. After drawing the line segment, with the help of compass we had to draw the perpendicular bisector of line segment AB. So, for that we measure the length of AB with compass and put the compass at point A, draw an arc on above and below the line segment AB.

3. Similarly draw the arc by placing compass on point B such that it cuts the arc drawn from point

4. Now, with the help of a ruler, join the intersection point of arcs to both points A and B that are above and below the line segment AB.

5. Name the intersection point of arcs above the line segment AB as C.

6. Now join point C with point A and point B with the help of the ruler.

7. Now, the equilateral triangle is ready. You can check each angle with the help of a protector and can also measure the length of all sides with the help of a ruler. It is the same for all sides and is equal to 4.5 cm.

Note: While doing construction, you should have a ruler, a compass, a protector. Also, do the construction carefully. Lack of concentration leads to improper construction. Always use a pencil to do construction because if in doing construction there is a mistake you can erase it easily, but while using a pen you can’t correct the mistake.