The midline theorem claims that cutting along the midline of a triangle creates a segment that is parallel to the base and half as long. Does that seem reasonable?
To prove the midline cut works, you need to use some geometry facts that you may already have encountered. If not, take some time to consider why these statements are true. Note 5
Fact 1: Vertical angles (the angles opposite each other when two lines intersect) are congruent (they have the same measure).
Why: We can show why, for example, m1 = m3:
m1 + m2 = 180° and m2 + m3 = 180°, since in both cases the two angles together create a "straight angle." So m1 + m2 = m2 + m3 = 180°. Subtracting m2 from each part of the equation, we see that
m1 = m3 = 180° - m2.