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
Construct a triangle, ABC in GSP. Then construct the
How do you think the area of triangle ABC compares
to the area of triangle ABC? to the area of triangle ABR? Make
Now find out if your conjecture is correct.
Select points A, B, and C. Under the "construct"
menu, choose polygon interior. Next, under the "measure"
menu choose area.
Now select points R, B, and C and complete the same
steps as above.
Select points A, B, and R and complete the steps again.
Now measure angle ACB. Move point B (make sure to
notice area while moving) so as to make a right triangle. Continue
to move point B to make an obtuse triangle.
Does you conjecture hold
for all types of triangles?
Construct all three Medians
Construct the other two medians of triangle ACB; median
CS and median AT.
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
Drag point B to various locations.
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
of the Centroid
Once again, drag point B so as to have an acute, right,
and obtuse triangle. Notice the location of the centroid. Is it
in the interior or exterior of triangle or both??
You should have noticed
that the centroid is always located in the interior of the triangle.
Now, construct the segment BG and GR and measure each
along with segment BR.
Set up a ratio of the smaller segments to the median
Notice the ratio. Drag point B to various locations.
What do you notice about the ratios?
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.
to Vicki Tarleton's Page