Assignment Four

Centers of a Triangle

Charles Meyer

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 Medial triangle.

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.


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