Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

Mid-segment Theorem


Date: 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/   
    
Associated Topics:
High School Geometry
High School Triangles and Other Polygons
Middle School Geometry
Middle School Triangles and Other Polygons

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/