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?

To divide a line segment $AB$ in the ratio $p: q$ ($p, q$ are positive integers),draw a ray $AX$ so that $\angle BAX$ is an acute angle and then mark points on ray $AX$ at equal distances such that the minimum number of these points is

To construct a triangle similar to a given $\triangle ABC$ with its sides $\frac{3}{7}$ of the corresponding sides of $\triangle ABC$,first draw a ray $BX$ such that $\angle CBX$ is an acute angle and $X$ lies on the opposite side of $A$ with respect to $BC$. Then locate points $B_{1}, B_{2}, B_{3}, \dots$ on $BX$ at equal distances and the next step is to join

Write True or False and give reasons for your answer.
By geometrical construction,it is possible to divide a line segment in the ratio $\sqrt{3}: \frac{1}{\sqrt{3}}$.

Draw a circle with the help of a circular bangle. Construct two tangents to this circle from a point in the exterior of the circle.

Draw $\Delta XYZ$ with $XY = 4\, cm$,$YZ = 6\, cm$,and $XZ = 7\, cm$. Then,construct $\Delta YMN$ similar to $\Delta XYZ$ with a scale factor of $\frac{4}{3}$. Write the steps of construction.