Geometry Chapter 5.4 Midsegment Theorem
A) Midsegment of a triangle - is a segment that connects the midpoints of two sides of a triangle.
B) Theorem: Midsegment Theorem - the segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long.
Example: given ΔABC with point D the midpoint of AC and point E the midpoint of BC and point F is the midpoint of AB, we can conclude
1) DE ll AB
2) DE = 1/2 AB
3) EF ll AC
4) EF = 1/2 AC
5) FD ll BC
6) FD = 1/2 BC
Therefore, you end up with 4 triangles that are congruent.
Check out websites dealing with Fractals- a fractal is created with midsegments. Beginning with any triangle, shade the triangle formed by the three midsegments. Continue this process for each unshaded triangle. Here is one: