Draw a right triangle ABC in which BC = 12 cm, AB = 5 cm and $\angle B= 90^{\circ}$.Construct a triangle similar to it and of scale factor $\frac{2}{3}$ . Is the new triangle also a right triangle ?

Solution
Given BC = 12cm, AB = 5 cm, $\angle B= 90^{\circ}$

Steps of construction
1.   Draw a line BC = 12 cm
2.   From B draw AB = 5 cm which makes an angle of $90^{\circ}$ at B.
3.   Join AC
4.   Make an acute angle at B as $< CBX$
5.   On BX mark 3 point at equal distance at $X_{1},X_{2},X_{3}$ .
6.   Join $X_{3}C$
7.   From $X_{2}$  draw $X_{2}{C}'\parallel X_{3}C$  intersect AB at ${C}'$
8.   From point ${C}'$  draw ${C}'{A}'\parallel CA$  intersect AB ${A}'$
Now  $\bigtriangleup {A}'B{C}'$ is the required triangle and  $\bigtriangleup {A}'B{C}'$  is also a right triangle.

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