Question

Construct a triangle of sides $5cm,6cm$ and $7cm$, then construct a triangle similar to it, whose sides are $\frac{2}{3}$ of corresponding sides of the first triangle.

Answer 1

Making the triangle

Draw a line segment AB = $5$ cm

Draw an arc at $6$ cm from point A.

Draw an arc at $7$ cm from point B so that it intersects the previous arc.

Joint the point of intersection from A and B.

This gives the required triangle ABC.

Dividing the base:

Draw a ray AX at an acute angle from AB

Plot three points on AX so that; $A{A}_1$ = $A_1{A}_2$ = $A_2{A}_3$

Join $A_3$ to B.

Draw a line from point $A_2$ so that this line is parallel to $A_3$B and intersects AB at point B'

Draw a line from point B' parallel to BC so that this line intersects AC at point C'

$\Rightarrow △A{B}^{\prime }{C}^{\prime }$ is the required triangle