**Definition: **The
median
of a triangle is the segment from a vertex to the midpoint of
the opposite side.

Instructions for Geometer's Sketch Pad Exploration

__Construct a Median and explore__

How do you think the area of triangle ABC compares to the area of triangle ABC? to the area of triangle ABR? Make a conjecture.

**Now find out if your conjecture is correct.
**

**Does you conjecture hold
for all types of triangles?**

__Construct all three Medians
and explore
__

**Do you notice anything about
the intersection of the three medians?**

*Since they all seem
to intersect at one point, let's see if this holds when the triangle
is changed.*

**Do the three medians keep
one intersection point when you drag point B?**

**Definition: **The three
medians do have a common intersection point called the centroid of
the triangle. The letter G
is used to represent the centroid of a
triangle.

__Characteristics
of the Centroid
__

*You should have noticed
that the centroid is always located in the interior of the triangle.*

*Can you make a conjecture
about how the centroid divides the median? Explore further to
see if this is true for the other two medians.*

Write a summary about the medians of a triangle and the centroid of a triangle.

**A** GSP animation modeling
all the concepts discussed in this assignment can be viewed after
completion of the summary assignment.