Question

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

Answer 1

Construction :

Step 1: Draw a line segment $AB$ of length $4.5$ cms.

Step 2: Take $4.5$ cms as radius and $A$ as center, draw an arc.

Step 3: Take $4.5$ cms as radius and $B$ as center, draw and arc.

Step 4: Let $C$ be the point where the two arcs intersect, join $AC$ and $BC$ and label the sides.

Thus, triangle $ABC$ is the required equilateral triangle.

Justification :

By construction, $AB=BC=CA$ ( Radius of equal arcs)

Since all sides are equal. Therefore, triangle $ABC$ is an equilateral triangle.

Thus, the construction is justified.