The Midsegment of a Triangle
In a triangle ABC if M is the middle of AB and N is the middle of CA then MN is called the midsegment of the triangle.
MN is parallel with BC and is also half the size of BC.
Let O be the symmetric of M in respect to N.
N is the middle of AC and the middle of MO. This means that AMCO is a parallelogram. So and .
But because M is the middle of BC we have that . So .
and A, M, B collinear means that .
and means that MBCO is a parallelogram.
MBCO is a parallelogram means that and . Because N is the middle of MO we have: