**Geometry Chapter 5.4 Midsegment Theorem**

**I) Vocabulary:**

**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:

http://mathforum.org/alejandre/applet.mandlebrot.html