Mid-segment TheoremDate: 02/02/99 at 19:55:07 From: Richard Phung Subject: Mid-segment theorem The Mid-segment theorem states that if a segment bisects two sides of a triangle then the segment is parallel and is half of the opposite side. Can you help me prove it? Thank you. Richard Phung Date: 02/03/99 at 02:37:03 From: Doctor Floor Subject: Re: Mid-segment theorem Hi Richard, I will give you a few hints that should make it possible to prove the theorem. You can go over writing a two-column proof yourself after that. Think of a triangle ABC, with D is the midpoint of AC and E is the midpoint of BC. C / \ D---E / \ A-------B Now draw a triangle D'E'C' that is twice as big as DEC beside ABC. C C' / \ / \ D---E / \ / \ / \ A-------B D'------E' Since D'C'= AC (length) and C'E' is BC (length) and angle C is angle C' we have that triangles ABC and D'E'C' are congruent (SAS). Since triangle DEC is half triangle D'E'C' we know that DE must be half the length of AB. Since D'E'C' is congruent to ABC, DEC is similar to ABC. So angle(CDE) is equal to angle A and DE must be parallel to AB. I hope this helps! Best regards, - Doctor Floor, The Math Forum http://mathforum.org/dr.math/ |
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