Are you my Median?
By Stephanie Britt
At first let us define what a median of a triangle is.
A midpoint of a segmant in a triangle is known as the median. If we create an equal lateral triangle where all sides and all angles are equal do the connections of the medians create an equal lateral triangle as well?
If we have triangle ABC
And we construct the medians at FGH
Then the triangle created by connecting the medians should be equilateral as well.
We can see here that the Larger triangle ABC is an equilateral triangle and if the medians are created then connected we get an equilateral triangle as well. We can also notice that the other triangles created are also equilateral as well.
If we try this with an Isosoceles triangle will the medians create an isosceles triangle too? With triangle FGH we see that HG and FH are congruent. When we create the medians and connect them does it create another Isosceles triangle? Are there any others?
We can see that four similar Isosceles triangles are created.
This is true for right triangles as well.
We can see that when the medians are constructed that another right triangle is created and one should notice that three other right triangles are created as well.
So medians of triangles help us to create similar triangles. Knowing how to create other similar triangles can help us when we want to discuss ratios of larger and smaller triangles. It can also help us create special triangles within special triangles.