# Ex.11.1 Q5 Constructions Solution - NCERT Maths Class 9

## Question

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

## Text Solution

**Reasoning:**

An equilateral triangle has three equal sides and three angles equal to \(60^\circ\).We know how to construct an angle of \(60^{\circ}\) **.**

**Steps of Construction:**

(i) Draw ray \(AB\)

(ii) With \(A\) as center and radius equal to \(3\;\rm{cm}\) draw an arc to cut ray \(AB\) at \(C\) such that \(AC= 3\;\rm{cm}\)

(iii) With \(C\) as the center and radius equal to \(AC\), draw an arc to intersect the initial arc at \(D\).

(iv) Join \(AD\) and \(AC\).

Thus,Triangle \(ADC\) is an equilateral triangle.

**Justification:**

\(\rm{AC = AD}\) (By construction since the radius of the arc is the same)

\(\rm{AC = CD}\) (By construction since the same radius was used again)

\(\therefore \rm{AC = AD = CD}\)

\(\therefore ADC\) is an equilateral triangle