Question

the centroid divides median in the ratio​

Answer 1

Answer:

1:2

Step-by-step explanation:

The Centroid of a Triangle Divides Each Median in the Ratio 1:2.

Answer 2

Answer:

I think 2:1

Step-by-step explanation:

Given G is centroid,

AD,BE,CF are median.

To Prove,

GD

AG

=

GE

BG

=

GF

CG

=

1

2

Construction : Produce AD to K such that AG=GK, join BK and CK

Proof : In △ABK,

F and G are mid points of AB and AK respectively

So, FG∥BK [by the mid point therom]

Hence we can say that GC∥BK ..... (A)

In △AKC

Similarly, BG∥KC ..... (B)

By (A) and (B)

BGCK is a parallelogram

In a parallelogram, diagonals bisect each other

So, GD=DK------(C)

AG=GK [By construction]

AG=GD+DK

So, AG=2GD [By (C)]

⇒

GD

AG

=

1

2

Thus, the centroid of the triangle divides each of its median in the ratio 2:1.