Question
Construct a triangle of sides 4cm, 5cm and 6cm and then a triangle similar to it whose sides are $\Big(\frac{2}{3}\Big)$ of the corresponding sides of it.
✓
Answer
Steps of construction:
Draw a line segment $B C=5 cm$.
With centre $B$ and radius 4 cm and with centre $C$ and radius 6 cm , draw arcs intersecting each other at $A$. Join $A B$ and $A C$. Then $A B C$ is the triangle.
Draw a ray $B X$ making an acute angle with $B C$ and cut off 3 equal parts making $B B_1=B_1 B_2=B_2 B_3$. Join $B_3 C$.
Draw $B ^{\prime} C ^{\prime}$ parallel to $B _3 C$ and $C ^{\prime} A ^{\prime}$ parallel to CA then $\triangle A ^{\prime} BC ^{\prime}$ is the required triangle.
Draw a line segment $B C=5 cm$.
With centre $B$ and radius 4 cm and with centre $C$ and radius 6 cm , draw arcs intersecting each other at $A$. Join $A B$ and $A C$. Then $A B C$ is the triangle.
Draw a ray $B X$ making an acute angle with $B C$ and cut off 3 equal parts making $B B_1=B_1 B_2=B_2 B_3$. Join $B_3 C$.
Draw $B ^{\prime} C ^{\prime}$ parallel to $B _3 C$ and $C ^{\prime} A ^{\prime}$ parallel to CA then $\triangle A ^{\prime} BC ^{\prime}$ is the required triangle.
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