Two sides $\mathrm{A}\mathrm{B}$ and $\mathrm{B}\mathrm{C}$ and median $\mathrm{A}\mathrm{M}$ of one triangle $\mathrm{A}\mathrm{B}\mathrm{C}$ are respectively equal to sides $\mathrm{P}\mathrm{Q}$ and $\mathrm{Q}\mathrm{R}$ and median $\mathrm{PN}$ of $∆\mathrm{P}\mathrm{Q}\mathrm{R}$ as shown in figure. Show that $∆\mathrm{ABM}\cong ∆\mathrm{PQN}$.

 
 

Two sides $\mathrm{A}\mathrm{B}$ and $\mathrm{B}\mathrm{C}$ and median $\mathrm{A}\mathrm{M}$ of one triangle $\mathrm{A}\mathrm{B}\mathrm{C}$ are respectively equal to sides $\mathrm{P}\mathrm{Q}$ and $\mathrm{Q}\mathrm{R}$ and median $\mathrm{PN}$ of $∆\mathrm{P}\mathrm{Q}\mathrm{R}$ as shown in figure. Show that $∆\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{}\cong ∆\mathrm{P}\mathrm{Q}\mathrm{R}$

In a huge park, people are concentrated at three points as shown in the figure.
A: Where there are different slides and swings for children.
B: near which a man made lake is situated.
C: Which is near to a large parking and exit.
Where should an ice-cream parlor be set up so that maximum number of persons can approach it?

Complete the hexagonal shaped rangolis by filling them with as many equilateral triangles of side 1 $\mathrm{cm}$ as you can. Count the number of triangles in each case. Which has more triangles?