Question

The centroid divides each medians of a triangle in the ratio ​

Answer 1

Answer:

Showing that the centroid divides each median into segments with a 2:1 ratio (or that the centroid is 2/3 along the median).

Answer 2

Step-by-step explanation:

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Asked on December 27, 2019 by

Savneet Ilyas

The centroid of a triangle divides each median in the ratio __________.

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ANSWER

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.

solution