Draw $\overline{AB}$ of length $10 \,cm$ and divide it in the ratio $3:8$ from $A$. Write the steps of construction.

Given a rhombus $ABCD$ in which $AB = 4 \, cm$ and $\angle ABC = 60^{\circ}$,divide it into two triangles,$ABC$ and $ADC$. Construct a triangle $AB'C'$ similar to $\triangle ABC$ with a scale factor of $\frac{2}{3}$. Draw a line segment $C'D'$ parallel to $CD$,where $D'$ lies on $AD$. Is $AB'C'D'$ a rhombus? Give reasons.

Draw a line segment $\overline{AB}$ of length $8\, cm$ and divide it in the ratio $2:3:5$ starting from point $A$. Write the steps of construction.

Write True or False and give reasons for your answer.
By geometrical construction,it is possible to divide a line segment in the ratio $2 \sqrt{3} : 2 \sqrt{3}$.

Write True or False and give reasons for your answer.
To construct a triangle similar to a given $\triangle ABC$ with its sides $\frac{7}{3}$ of the corresponding sides of $\triangle ABC$,draw a ray $BX$ making an acute angle with $BC$ and $X$ lies on the opposite side of $A$ with respect to $BC$. The points $B_{1}, B_{2}, \dots, B_{7}$ are located at equal distances on $BX$,$B_{3}$ is joined to $C$ and then a line segment $B_{6}C'$ is drawn parallel to $B_{3}C$ where $C'$ lies on $BC$ produced. Finally,line segment $A'C'$ is drawn parallel to $AC$.

Draw a triangle $ABC$ in which $AB = 5 \, cm$,$BC = 6 \, cm$ and $\angle ABC = 60^{\circ}$. Construct a triangle similar to $\triangle ABC$ with a scale factor of $\frac{5}{7}$. Justify the construction.