We consider the triangle below.

If we draw a segment from each vertex to the opposite
side's midpoint, we find that in the above
case, a common point of intersection occurs in the
center of the triangle. This is defined as the
Centroid, G. You'll notice that all three segments
are concurrent to the Centroid and G appears to be
the *center* of the triangle....

__Things to try with the a triangle and a given
centroid__
(solutions below)

**Question 1** Is it always the case that these lines from
each vertex to the midpoint to the opposite

sides are concurrent to G ?

**Question 2 **Would a triangle's moment or center of mass
(if uniformly massive & dense) be the

location of the Centroid?

**Question 3 **If we can draw a circle inside a triangle
that is tangent to all three sides, what is the relaionship

between the radius of the triangle and the centroid?
(hint: construct the circle then explore the triangles
that can exist with it have each side tangent to the circle)

To try the above problems out and any others using
*Geometry Sketchpad 4.0* with the tool below

**Click here to explore
the triangle with a GSP 4.1 centroid tool**

Solutions to above questions
1. yes

2. yes

3. Answers vary

Proofs and other implications are left to the reader and are
classic explorations for high school students.

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