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Example 1

Construct a triangle similar to a given triangle ABC with its sides equal to 3/4 of the corresponding sides of the triangle ABC (i.e. of scale factor 3/4).

Given scale factor = 3/4

Steps of Construction :

  1. Draw any ray BX making an acute angle with BC on the side opposite to the vertex A.
  2. Locate 4 (the greater of 3 and 4 in 3/4 )  points B_1,B_2,B_3 and B_4 on   BX so that 〖BB〗_1=B_1 B_2=B_2 B_3=B_3 B_4.
  3. Join B_4C and draw a line through B_3 (the 3rd point, 3 being smaller of 3 and 4 in 3/4) parallel to B_4 C to intersect BC at C′.
  4. Draw a line through C′ parallel to the line CA to intersect BA at A′.

Thus, Δ A′BC′ is the required triangle



BC^′/BC=(BB_3)/(BB_4 )=3/4.

Also, A’C’ is parallel to AC

So, the will make the same angle with line BC

∴ ∠ A’C’B = ∠ ACB


In Δ A’BC’ and ABC

∠ B = ∠ B

 ∠ A’C’B = ∠ ACB


Since corresponding sides of
similar triangles are in the same ratio

 (A^′ B)/AB=(A^′ C^′)/AC=(BC^′)/BC

So, (A^′ B)/AB=(A^′ C^′)/AC=(BC^′)/BC =3/4 .

This justifies the construction.


  1. Chapter 11 Class 10 Constructions
  2. Concept wise
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CA Maninder Singh
CA Maninder Singh is a Chartered Accountant for the past 7 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .