Centers of a Triangle
As a study of centers of triangles, I selected the Medial
triangle. I am interested in understanding how a Medial triangle
is exactly one-fourth the area of the original triangle it is
formed from. I also thought this would be beneficial for my 7th
grade students who are currently learning about the area of a
triangle. To begin, I need to create a triangle of any size.
I will now need to find the midpoints of the segments of the
triangle. I will label these midpoints with lower case letters
to designate the Medial triangle.
These midpoints: d, e, f, will now be connected to form the
I need to find if the Medial triangle is actually one-fourth
the size of the original.
The Medial triangle seems to be one-fourth the size of the
original, but the use of the GSP calculator will help verify.
So, if a Medial triangle is created within any triangle, the
Medial triangle's area will always be one-fourth the original.