Step by step
The question
Question: A D is a median of triangle A B C and G is where the medians meet, with AD = 9: find GD.
1 Use the median rule
A median goes from a corner to the middle of the opposite side.
D is the middle of B C.
The three medians all meet at one point, G.
It is called the centroid.
G cuts each median into 2 parts and 1 part: the long part from the corner.
2 Find one part
A D is 3 equal parts: 2 for A G and 1 for G D.
9 divided by 3 is 3.
one part = 9 ÷ 3 = 3
Careful!
G is not the middle of the median.
A G is 2 parts out of 3.
Careful: not AG = 4.5 ✗
3 Find GD
GD is 1 part: 3.
GD = 3
4 Check
Let's check: A G plus G D is 9, the whole median.
And A G is twice G D.
So it is right!
AG + GD = 6 + 3 = 9 = AD, 6 = 2 × 3
Let's look back.
First: use the median rule.
Then: find one part.
Then: find GD.
Last: check.
Answer
GD = 3