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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.

Sketchpad

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 triangle also.

Go back to sketchpad above and investigate #2.

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?

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