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

**Solution:**

An equilateral triangle has three equal sides and three angles equal to 60º each.

Steps of Construction:

- Draw a ray AB.
- With A as center and radius equal to 3 cm, draw an arc to cut ray AB at C such that AC = 3 cm
- With C as the center and radius equal to AC (3cm), draw an arc to intersect the initial arc at D.
- Join AD and DC.
- Triangle ADC is an equilateral triangle with sides of 3cm each.

Justification:

AC = AD (By construction since the radius of the arc is the same)

AC = CD (By construction since the same radius was used again)

Hence AC = AD = CD = 3cm

Thus, ADC is an equilateral triangle.

**Video Solution:**

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

### Maths NCERT Solutions Class 9 - Chapter 11 Exercise 11.1 Question 5:

**Summary:**

It is given that we have to construct an equilateral triangle upon the given side. We have drawn the triangle using a compass and ruler and justified the construction.