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

Given that, scale factor = 3 4 To construct a triangle A B C and a similar triangle A ' B C ' , in which each side of △ A ' B C ' is 3 4 th of corresponding sides of △ A B C . Step of construction: Step 1 . Draw a △ A B C . Step 2 . On B draw an acute angle ∠ C B X downwards. Step 3 . Along B X , mark 4 points B 1 , B 2 , B 3 and B 4 such that B B 1 = B 1 B 2 = B 2 B 3 = B 3 B 4 . Step 4 . Join B 4 C . Step 5 . From B 3 , draw B 3 C ' parallel to B 4 C (draw an angle equal to ∠ B B 4 C ), meeting B C in C ' , such that B C ' is 3 4 of B C . Step 6 . From C ' , draw A ' C ' parallel to A C (draw an angle equal to ∠ A C B ), meeting A B in A ' , such that A ' B is 3 4 of A B . Then △ A ' B C ' is the required triangle whose sides are 3 4 th of the corresponding sides of the △ A B C .

Draw a triangle A B C with side B C = 3 . 5 cm , A B = 3 . 5 cm and ∠ A B C = 60 ∘ . Then construct a triangle whose sides are 3 4 of the corresponding sides of the triangle A B C .

Given that, B C = 3 . 5 cm , A B = 3 . 5 cm , ∠ A B C = 60 ∘ and scale factor = 3 4 . We have to construct a triangle A B C and a similar triangle A ' B C ' , in which each side of △ A ' B C ' is 3 4 th of corresponding sides of △ A B C . Step of construction: Step 1 . Take B C = 3 . 5 cm . Step 2 . At B draw an angle ∠ P B C = 60 ∘ . Step 3 . From point B draw an arc of 3 . 5 cm , intersecting the ray B P at A . Step 4 . Join A C . Then A B C is the required triangle. Step 5 . On B draw an acute angle ∠ C B X downwards. Step 6 . Along B X , mark 4 points B 1 , B 2 , B 3 and B 4 such that B B 1 = B 1 B 2 = B 2 B 3 = B 3 B 4 . Step 7 . Join B 4 C . Step 8 . From B 3 , draw B 3 C ' parallel to B 4 C (draw an angle equal to ∠ B B 4 C ), meeting B C in C ' , such that B C ' is 3 4 of B C . Step 9 . From C ' , draw A ' C ' parallel to A C (draw an angle equal to ∠ A C B ), meeting A B in A ' , such that A ' B is 3 4 of A B . Then △ A ' B C ' is the required triangle whose sides are 3 4 th of the corresponding sides of the △ A B C .

Construct a triangle with sides 2 . 4 cm , 1 . 8 cm and 2 . 1 cm and then construct a triangle whose sides are 3 4 of the corresponding sides of the first triangle.

Given that, the three sides of a triangle are 2 . 4 cm , 1 . 8 cm , 2 . 1 cm and scale factor = 3 4 . We have to construct a triangle A B C and a similar triangle A ' B C ' , in which each side of △ A ' B C ' is 3 4 th of corresponding sides of △ A B C . Step of construction: Step 1 . Take B C = 2 . 4 cm . Step 2 . From point B draw an arc of 2 . 1 cm and from point C draw an arc of 1 . 8 cm , cutting each other at point A . Step 3 . Join A B and A C . Then A B C is the required triangle. Step 4 . On B draw an acute angle ∠ C B X downwards. Step 5 . Along B X , mark 4 points B 1 , B 2 , B 3 and B 4 such that B B 1 = B 1 B 2 = B 2 B 3 = B 3 B 4 . Step 6 . Join B 4 C . Step 7 . From B 3 , draw B 3 C ' parallel to B 4 C (draw an angle equal to ∠ B B 4 C ), meeting B C in C ' , such that B C ' is 3 4 of B C . Step 8 . From C ' , draw A ' C ' parallel to A C (draw an angle equal to ∠ A C B ), meeting A B in A ' , such that A ' B is 3 4 of A B . Then △ A ' B C ' is the required triangle whose sides are 3 4 th of the corresponding sides of the △ A B C .