Construct a tria

The steps involved are:

Step 1: Draw a line segment AB = 4.2 cm.

Step 2: Taking A as center, draw an arc of radius 6.2 cm. Then, take B as center and draw an arc of radius 5 cm. These arcs will intersect at point C (say). Join AC and BC, such that AC = 6.2 cm and BC = 5 cm. Thus, ∆ABC is the required triangle.

Step 3: Draw a ray AX making acute angle with straight line AB to the opposite side of vertex C.

Step 4: Locate 3 points on ray AX, namely A ₁ , A ₂ and A ₃ (since 3 is greater among 2 and 3) such that, AA ₁ = A ₁ A ₂ = A ₂ A ₃ .

Step 5: Join BA ₃ and then draw a line through A ₂ such that it is parallel to BA ₃ and intersects on AB at B’.

Step 6: Now draw a line through B’ such that it is parallel to BC and intersects on AC at C’.

∆AB’C’ is the required triangle with sides 2/3 of the corresponding sides of ∆ABC.