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# 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.

**☛ Check: **NCERT Solutions for Class 9 Maths Chapter 11

**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.

**☛ Related Questions:**

- Construct an angle of 90° at the initial point of a given ray and justify the construction.
- Construct an angle of 45° at the initial point of a given ray and justify the construction.
- Construct the angles of the following measurements:(i) 30°(ii) 22(1/2)°(iii) 15°
- Construct the following angles and verify by measuring them by a protractor:(i) 75°(ii) 105°(iii) 135°

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