Answer:To prove the relationship about the length of a midsegment, I can use the properties of parallel lines and transversals. If I draw at least two midsegments, I see that they form congruent triangles within the original triangle, ∆ABC. I can prove the congruence of these triangles using triangle congruence criterion, and then use properties of congruent triangles and the Transitive Property to show that the length of the midsegment is half the length of the side it is parallel to.
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