Question

What is "Centroid of a triangle" and why is it important?

Answer 1

The Centroid of a triangle is where the medians of a triangle intersect

Answer 2

Medians? O__O

Answer 3

The physical importance is that the centroid is the "center of gravity" for the triangle. This means that if you balance the triangle on a pencil or your finger, then it will be perfectly balanced on the center of gravity (centroid).

Answer 4

? Um....I'm sorry. I'm not following you all that well.

Answer 5

ok hold on ill break it down

Answer 6

check out some cool stuff about centroids:

http://www.mathopenref.com/trianglecentroid.html

Answer 7

the word centroid means the geometric center of the object's shape

Answer 8

Geometric center?

Answer 9

open the link I posted, and look for the word "plate" on that page

Answer 10

Where on the page, Fiddle? The lower left?

Answer 11

look for where it says:
Refer to the figure on the right. Imagine you have a triangular metal plate ...

Answer 12

The triangle? O___O

Answer 13

do you see a picture of a triangular plate balanced on top of a pencil ?

Answer 14

?! Um, yes Fiddle. :)

Answer 15

well, read what it says on the page.
you can also play with the triangle on top of the page to see what happens to the centroid.

when you're done reading and studying the page, we can address any question you have about it
:)

Answer 16

Fiddle, so the angles stay the same no matter where you pull the dots? Is that why it is congruent? Or is it the sides? O___O

Answer 17

so what do you need help with?

Answer 18

I don't really understand what a Centroid of a triangle is. I know it is in the middle, but at the moment I'd like to know about my question that I posted above yours.

Answer 19

This one "Fiddle, so the angles stay the same no matter where you pull the dots? Is that why it is congruent? Or is it the sides? " ???

lol a question within a question

Answer 20

Yup, that's the one. ^__^

Answer 21

ok

Answer 22

well as you play with the interactive drawing, the angles of the triangles do change


however, the medians will always intersect at one point (no matter what the triangle is) and this point is the centroid

Answer 23

imagine trying to balance this triangle on a very very sharp point

Answer 24

it will be perfectly balanced if you place this sharp point at the centroid

Answer 25

"however, the medians will always intersect at one point (no matter what the triangle is) and this point is the centroid" ~Jim Can you explain the "medians"? And the point where they all intersect is centroid?

Answer 26

yay centroids ! (sounds like some kind of vitamins) :)

Answer 27

ok, let's define what a median is

Answer 28

when you drive down the road, you're often driving by a median right?

Answer 29

Median, meaning in the middle of the road/lane you are in? Um...yes.

Answer 30

exactly

Answer 31

so a single median divides a triangle into two equal halves

Answer 32

and it does this by starting at one vertex (the sharp point on a triangle) and it cuts this angle in half

Answer 33

so if this triangle was an actual object, then half of the mass is on one side of the median and half of the mass is on the other side

Answer 34

Vetex is this?