For this investigation, we will look at
three basic triangles (equilateral, isosceles, and right) and their respective
medial triangles. The resulting medial triangles is of interest in each
of these. Read below to see what appears to be evidence, but then go to
sketchpad to make your own conclusions for each.
The triangle given below is an equilateral
triangle. When the medial triangle is constructed, it appears to also be
equilateral. But as you know, we cannot assume that this holds for all cases
without further investigation.
Click on sketchpad above, go to #1, follow
directions to view all cases for the equilateral triangle. What is your
conclusion? Does the medial triangle hold as an equilateral triangle also?
The triangle shown below is an isosceles
triangle and once again, its medial triangle appears to be an isosceles
Go back to sketchpad above and investigate
What are the results? Do you know why?
Begin to formulate ideas to make a final conclusion.
The following is a right triangle. Given
the figure below, the medial triangle is a right triangle.
Go to sketchpad- #3 to investigate.
Does the medial triangle remain as a right
triangle, no matter where you move each vertice?
Recall how the median compares with the
side it is parallel with.
If you are unsure, go to sketchpad and
investigate the distance.
What is your conclusion?
By now, you should be have a good idea
of why the medial triangles remain as the same type of triangle as the original.
What do you think?
Since the medians of the triangle are one-half
the length of its parallel side, then the medial triangles become similar
with our original triangles.
Do you know which similarity postulate holds for
the above statement?