Figure 1 shows Δ ABC with D and E as midpoints of sides AC and AB respectively. If you look at this triangle as though it were a trapezoid with one base of BC and the other base so small that its length is virtually zero, you could apply the “median” theorem of trapezoids, Theorem 55.
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 , by Theorem 56,
Hope the above explanation helped you, now let me on properties of trapezoids.
