Draw a triangle ABC with side BC = 6 cm, 
. Then construct another triangle whose sides are 
times the correspo0nding sides of 
To construct a right-angled triangle such that its sides are 2/3 times of the corresponding sides of the given triangle:
(a). Draw a line BC = 6 cm as base.
(b). Taking BC as base.
(c). Draw 30° from C angled as ∠BCA = 30°, and draw a line through it.
(d). Let ∠ABC = x,
The total sum of all angles of a triangle is 180°. ⇒ 30° + 105° + x = 180°
x + 135° = 180° ⇒ x = 180° - 135° = 45°
Draw an arc 45° from B and extend the line BA, cutting CA at A.
We have got ∆ABC.
Now we shall construct another triangle whose sides are 2/3 times the corresponding sides of the triangle.
(e). Set the compass to 1 cm, rest one of the legs of the compass at point B and start making arcs B1 starting from B, B2 from B1 and B3 from B2, since we have to construct a triangle having side equal to 2/3 times of corresponding sides of the given triangle.
(e). Join B3 to C.
(f). Now, draw a line to BC from B2, parallel to CB3.
(g). Say this point on BC is C’.
(h). Similarly, make an arc from C’ and cut the arc of 30° from its foot, then join C’A’(say).
(i). We get BA’ automatically.
And hence, we have the required triangle BA’C’.
