Question
Draw a right triangle ABC in which BC = 12cm, AB = 5cm and $\angle\text{B}=90^\circ.$ Construct a triangle similar to it and of scale factor $\frac{2}{3}.$ Is the new triangle also a right triangle?
✓
Answer
Steps of construction:
Draw a line segment BC = 12cm,
From 6 draw a line AB = 5cm which makes right angle at B.
Draw a line segment BC = 12cm,
From 6 draw a line AB = 5cm which makes right angle at B.
3. Join $A C, \triangle A B C$ is the given right triangle.
4. From B draw an acute $\angle CBY$ downwards.
5. On ray $B Y$, 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 $B C$ at $N$.
8. From point $N$ draw $N M \| C A$ intersect $B A$ at $M . \triangle M B N$ is the required triangle. $\triangle M B N$ is also a right angled triangle at B .
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