
Steve S. answered 12/12/13
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Tutoring in Precalculus, Trig, and Differential Calculus
Check out http://www.regentsprep.org/Regents/math/geometry/GP10/MidLineL.htm
If two triangles have the same shape but different sizes (i.e., are similar), their corresponding sides are proportional.
If ΔABC ~ ΔDEF, then AB/BC = DE/EF; or CA/FD = BA/ED; etc.
A midsegment creates a smaller but similar triangle inside the original triangle. Each side of the smaller triangle is 1/2 the length of the corresponding side in the larger triangle.