Question

Construct a triangle of sides $4cm,5cm$ and $6cm$ and then a triangle similar to it whose sides are $\frac{2}{3}$ of the corresponding sides of the first triangle.

Answer 1

Steps of construction:

1. Draw a base $BC$ of length $6cm$.

2. Place the pointed end of the compass on $B$ and mark an arc of radius $5cm$. Now, place the pointed end on $C$ and mark an arc of radius $4cm$ intersecting with the previous arc. Mark this intersection point as $A$.

3. Join $A-B$ and $A-C$. $△ABC$ is the first triangle.

4. Draw a ray $BX$ from point $B$ on opposite side of $A$ to line $BC$.

5. Mark three equidistant points on ray $BX$ and name them $B_1,B_2$ and $B_3$.

6. Join $B_3-C$. From $B_2$, draw a line parallel to $B_{3}C$ and let it intersect $BC$ in $D$. From $D$ draw a line parallel to $AC$ and let it intersect $AB$ in $E$.

$△BED$ is the required similar triangle.