Question

Draw a right angled ∆ XYZ. Draw its medians and show their point of concurrence by G.

Answer 1

Steps of construction :
(i) Draw a right angled ∆XYZ.
(ii) Draw the perpendicular bisector PQ of side YZ that intersect YZ at L.
(iii) Join XL. XL is the median to the side YZ.
(iv) Draw the perpendicular bisector TU of side ZX that intersect YZ at M.
(v) Join YM. YM is the median to side ZX.
(vi) Draw the perpendicular bisector RS of side XY that intersect XY at N.
(vii) Join ZN. ZN is the median to the side XY.
Hence, ∆XYZ is the required triangle in which medinas XL, YM and ZN to the sides YZ, ZX and XY respectively intersect at G.
The point G is the centroid of ∆XYZ.