## EMAT 6680 Assignment #6

## Explorations with Geometers Sketchpad

#### by Kent Wiginton

We want to construct a triangle and its medians. Since we have
our library of GSP sketches then we can just find the sketch of
the Centroid and play that sketch to get the triangle and its
centroid. (Just hide the centroid we will not need it for this
exercise.) To make things easy for discussion we will color each
median a different color.

Our objective in this exercise is to construct a different
triangle with the sides equal to the medians of the original triangle.
My first thought was that I needed to use circles with radius
equal to each of the medians. We need to construct a point p outside
the original triangle and make p the center of our first circle.
We can construct this circle by first picking point p and then
highlighting the a median and then selecting the *circle by
center+ radius *construction in the construct menu. We will
keep our color code through out the assignment. Now we want to
make a circle for each of the medians. However we cannot forget
the purpose of the exercise: to make another triangle. Lets build
the triangle as we go. Construct the next circle with the center
on the first circle. We first construct a point on the red circle
and then construct the circle just as before. Now where would
we need to place the third center? Remember we want to make a
triangle. I want the circles to intersect so that each side will
be a radius of a different circle.

Now that we have our three intersections lets construct the
triangle.

Click **here** to see a gsp script
of the entire process.

Some interesting observations that I made concern the areas
of the different triangles. I observed that the area of the new
triangle is exactly 75% of the original triangle.

Click **here** and see for yourself.

**Return**