Assignment #6

By Nikki Masson

Explorations with Geometer's Sketchpad

 

Are the medial triangle similar to the original triangle?

In this exploration, we will explore triangles and the relationship between certain triangles. First we will construct a triangle and its medians. Then we will draw the medial triangle using GSP. The medial triangle is the triangle formed by the line segments joining the three medians of a triangle.

 

Our medial triangle is the yellow triangle above.

Let's see if the triangle ABC is similar to triangle DFE. For these two triangles to be similar they would need to meet the following criteria:

* two pairs of corresponding angles are congruent (therefore the third pair of corresponding angles are also congruent)
* the three pairs of corresponding sides are proportional.

As we can see the angles are congruent, now let's see if the sides are proportional. The following are the lengths of the sides of the triangles and then we will calculate the ratios:

 

Now we calculate the ratios and see if the two triangles are proportional.

Conclusion: The medial triangle and the original triangle are similar.

If you would like to explore more about the relationship between the medial triangle and the original triangle, use the GSP link below:

Construction of Medial Triangle

 

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