Figure 1 *ABC* with *D* and *E* as midpoints of sides * AC *and

*respectively. If you look at this triangle as though it were a trapezoid with one base of*AB

*and the other base so small that its length is virtually zero, you could apply the “median” theorem of trapezoids,*BC

*Theorem 55.*

* Figure 1 T*he segment joining the midpoints of two sides of a triangle.

*Theorem 56 (Midpoint Theorem):* The segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side.

In Figure 1*Theorem 56,*

**Example 1:** In Figure 2*HJ.*

**Figure 2 **Compute the length of the broken line segment joining the midpoints of two sides of the triangle.

Because *H* and *J* are midpoints of two sides of a triangle:

True or False: All triangles are convex

What is the degree measure of the interior angle determined by two adjacent sides of a regular decagon?

144°