Answer
1. Since the midpoint forms a triangle is inside the outer triangle, is has the same angles as the outer triangle. By AAA, these two triangles are similar.
2. Since it is at the midpoint, its two sides are half the length of the sides of the larger triangle.
3. Thus, the base, which is the diagonal that connects the two midpoints, is half of the length of the third side, for similar triangles have the same proportions.
