Question

Question 2
Draw a right $\Delta$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?
Thinking process
Here scale factor $\frac{m}{n}=\frac{2}{3}$ i.e m < n then the triangle to be constructed smaller than the given triangle Use this concept and then construct the required triangle.

Answer 1

Steps of construction
1. Draw a line segment BC = 12 cm
2. From B draw a line AB = 5cm which makes a right angle at B.

Constructions
3. Join AC, $\Delta$ ABC is the given right triangle.
4. From B draw an acute $\angle$ CBY downwards
5. On ray BY mark three points $B_1,B_2$ and $B_3$ such that $B{B}_1=B_1{B}_2=B_2{B}_3$
6. Join $B_{3}C$
7. From point $B_2$ draw $B_{2}N||B_{3}C$ intersect BC at N
8. From point N draw NM || CA intersect BA at M $\Delta$ MBN is the required triangle $\Delta$ MBN is also a right angled triangle at B.