Draw an equilateral triangle $ABC$ with each side $4\, cm$. Construct a triangle similar to it with a scale factor of $\frac{3}{5}$. Is the new triangle also equilateral?

Draw $\overline{ AB }$ of length $5.9\,cm$ and divide it in the ratio $5: 7$ from $A$.

Draw a line segment of length $7 \, cm$. Find a point $P$ on it which divides it in the ratio $3: 5$.

To divide a line segment $AB$ in the ratio $4:7,$ a ray $AX$ is drawn first such that $\angle BAX$ is an acute angle and then points $A_1, A_2, A_3, \dots$ are located at equal distances on the ray $AX$ and the point $B$ is joined to:

Draw $\Delta PQR$ with $m \angle P=60^{\circ}, m \angle Q=45^{\circ}$ and $PQ =6 \text{ cm}$. Then construct $\Delta PBC$ similar to $\Delta PQR$ whose sides have lengths $\frac{5}{3}$ times the lengths of the corresponding sides of $\Delta PQR$.

Draw $\Delta ABC$ with $AB = 6 \, cm$,$BC = 8 \, cm$,and $m\angle B = 60^\circ$. Then,construct $\Delta BXY$ similar to $\Delta ABC$ whose sides have lengths $\frac{4}{5}$ times the lengths of the corresponding sides of $\Delta ABC$. Write the steps of construction.