Construct a trian

Step 1. At first drawn a base line BC of length 5.5 cm with the help of scale.

Step 2. Taking B as center draw an arc of radius 5 cm with the help of compass. Similarly taking C as center draw a arc of radius 6.5 cm with the help of compass.

Join AB and AC thus completing the triangle ABC.

Step 3. A ray BX is drawn making an acute angle with BC opposite to vertex A. Five points B₁ , B₂ , B₃, B₄, and B₅ at equal distance is marked on BX.

Step 4. B₃ is joined with C to form B₃ C as 3 point is smaller. B₅ C₁ is drawn parallel to B₃ C as 5 point is greater.

Step 5:C₁A₁is drawn parallel to CA.

Thus, A₁BC₁ is the required triangle.

Justification:

Since the scale factor is ,

We need to prove,

By construction,

… (1)

Also, A₁C₁ is parallel to AC.

So, this will make same angle with BC.

∴ ∠A₁C₁B = ∠ACB …. (2)

Now,

In ΔA₁BC₁ and ΔABC

∠ B = ∠ B (common)

∠A₁C₁B = ∠ACB (from 2)

ΔA₁BC₁∼ ΔABC

Since corresponding sides of similar triangles are in same ratio.

From (1)

Hence construction is justified.