In figure 5.23, G is the point of concurrence of medians of ΔDEF. Take point H on ray DG such that D-G-H and DG = GH, then prove that

Given G is the point of concurrence of medians of Δ DEF so the medians are divided in the ratio of 2:1 at the point of concurrence. Let O be the point of intersection of GH AND EF.

The figure is shown below:

⇒ DG = 2 GO

But DG = GH

⇒ 2 GO = GH

Also DO is the median for side EF

⇒ EO = OF

Since the two diagonals bisects each other

⇒ GEHF is a ∥gram.