Draw a right angled XYZ. Draw it's medians and show their point of concurrence by G.

(i) Draw a right angled $\Delta X Y Z$.

(ii) Draw the perpendicular bisector PQ of side $\mathrm{YZ}$ that intersect $\mathrm{YZ}$ at $\mathrm{L}$.

(iii) Join XL. XL is the median to the side YZ.

(iv) Draw the perpendicular bisector TU of side $Z X$ that intersect $Y Z$ at $M$

(v) Join YM. YM is the median to side $Z X$.

(vi) Draw the perpendicular bisector RS of side XY that intersect XY at N.

(vii) Join ZN. ZN is the median to the side $X Y$. Hence, $\Delta \mathrm{XYZ}$ is the required triangle in which medians $\mathrm{XL}, \mathrm{YM}$ and $\mathrm{ZN}$ to the sides $\mathrm{YZ}, \mathrm{ZX}$ and $\mathrm{XY}$ respectively intersect at G.

The point G is the centroid of $\Delta X Y Z$.