In the given triangle $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$ are the mid points of sides $\mathrm{AB}, \mathrm{BC}$ and $\mathrm{AC}$ respectively. Prove that triangle $\mathrm{PQR}$ is similar to triangle $\mathrm{ABC}.$

In the following figure, $\mathrm{AD}$ and $\mathrm{CE}$ are medians of $△\mathrm{ABC}.$ $\mathrm{DF}$ is drawn parallel to $\mathrm{CE}.$
Prove that: $\mathrm{EF} = \mathrm{FB},$

In the following figure, $\mathrm{AD}$ and $\mathrm{CE}$ are medians of $△\mathrm{ABC}.$ $\mathrm{DF}$ is drawn parallel to $\mathrm{CE}.$
Prove that: $\mathrm{AG} : \mathrm{GD} = 2 : 1.$

The ratio between the altitudes of two similar triangles is $3 : 5;$ write the ratio between their:

medians.
 

The ratio between the altitudes of two similar triangles is $3 : 5;$ write the ratio between their:
perimeters,
 

The ratio between the altitudes of two similar triangles is $3 : 5;$ write the ratio between the
areas.
 

The ratio between the areas of two similar triangles is $16 : 25.$ Find the ratio between their :

perimeters,
 

The ratio between the areas of two similar triangles is $16 : 25.$ Find the ratio between their :

altitudes,