Question

Prove that any two medians of a triangle divide each other in the ratio 2:1.

Answer 1

You know that this is a Mathematical question, wright?

Answer 2

yaa i knew by mistake instead of posting in geometry i posted it in geography
but if u know it u can answer

Answer 3

1) Let the triangle be ABC; E be the mid point of CA and F be the mid point of AB; Join the medians BE and CF; let them intersect at G; also join EF.

2) Consider triangles, GFE and GBC:

i) <FGE = <BGC [Vertically opposite angles]

ii) <GFE = <GCB [Alternate interior angles are equla; In a triangle line joining the midpoints of any two sides is parallel to the third side and half of the third side; as such here, EF is parallel to BC and half of BC]

iii) Hence triangle GEF is similar to triangle GBC. [AA similarity axiom].

3) Hence of the above, the corresponding sides are in proportion;

that is: GE/GB = GF/GC = EF/BC

But EF/BC = 1/2 [Since EF is half of BC from the reason given in 2-ii]

==> GE/GB = GF/GC = 1/2;

Thus the centroid G divides each median in the ratio 2:1

Answer 4

"In a triangle line joining the midpoints of any two sides is parallel to the third side and half of the third side."
Is it not the mid point theorem