In the given triangle p,Q and R are the midpoints of sides AB, BC and AC respectively. Prove that triangle PQR is similar to triangle ABC.

Dear Student,

Since P, Q, R are mid-points of AB, BC, AC by mid-point theorem :
$\Rightarrow$PR = $\frac{1}{2}$BC    $\Rightarrow$$\frac{\mathrm{PR}}{\mathrm{BC}}$ = $\frac{1}{2}$  ................. (1) 
$\Rightarrow$PQ = $\frac{1}{2}$AC   $\Rightarrow$$\frac{\mathrm{PQ}}{\mathrm{AC}}$ = $\frac{1}{2}$   ................. (2)
$\Rightarrow$QR = $\frac{1}{2}$AB   $\Rightarrow$$\frac{\mathrm{QR}}{\mathrm{AB}}$ = $\frac{1}{2}$   .................. (3)
Now, In triangle PQR and triangle CAB
$\Rightarrow$$\frac{\mathrm{PR}}{\mathrm{BC}}$ = $\frac{\mathrm{PQ}}{\mathrm{AC}}$ = $\frac{\mathrm{QR}}{\mathrm{AB}}$              (From (1) , (2) and (3) )
Therefore, the two triangle are similar SSS test

Regards