Question

construct an equilateral triangle given its side of length of 4.5 cm and justify the construction

Answer 1

Take base as BC = 4.5 cm
Construct Angle B = 60° ( Since, all the angles of an equalateral triangle is 60°)
Then cut an arc of 4.5 cm on B as mark it as A
then join AB

Answer 2

Steps:-

$\rightarrow$Draw a line segment AB=4.5cm

$\rightarrow$With B and A as centres draw two arcs of radius 4.5cm meeting at C.

$\rightarrow$Join C to A and B.

$\rightarrow$$\Delta$ABC is the required triangle.

Justification:-

In ∆ABC

AB=AC $\implies$$\angle$C=$\angle$B

Also AB=BC $\implies$$\angle$C=$\angle$A

Hence $\angle$A=$\angle$B=$\angle$C

But $\angle$A+$\angle$B+$\angle$C=180°

$\angle$A=$\angle$B=$\angle$C=$\frac{180°}{3}$=60°