Comparing Medial Triangles of Equilateral, Isosceles, and Right Triangles
If a triangle is an equilateral triangle, then the triangle formed by the midpoints is also an equilateral triangle.
But, what can we conclude about triangles other than equilateral triangles?† Letís explore this idea with isosceles triangles.
As we can see, the medial triangle formed from an isosceles triangle is also an isosceles triangle.
What about right triangles?
Again, we see the medial triangle formed from a right triangle is also a right triangle.
For an arbitrary triangle, we can construct the triangle formed by the medians.†
Given triangle DEF with midpoints A, B, and C, we know segment AB is parallel to EF by the Midsegment Theorem.† Furthermore, we know BC is parallel to DE for the same reason; and AC is also parallel to DF.† Since the medial is constructed from the midpoints of each side of the triangle, we also know that each side is half its length.† Therefore, the medial triangle formed is similar since the side lengths are proportional.