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Geometry Proof

 
 
Reply Mon 24 Jan, 2005 11:29 pm
Find as many ways to prove the following statement:

Prove that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.
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Type: Discussion • Score: 1 • Views: 1,095 • Replies: 8
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Bibliophile the BibleGuru
 
  1  
Reply Tue 25 Jan, 2005 05:44 am
Three vertices? How does that work - or am I missing something?
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engineer
 
  1  
Reply Tue 25 Jan, 2005 08:53 am
Re: Geometry Proof
P.a.t.t.i wrote:
Find as many ways to prove the following statement:

Prove that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.


I won't solve your homework for you, but I will give you a hint. Turn right triangle ABC into rectangle ABCD. Let the midpoint of the hypotenuse be point E. If BC is the hypotenuse of ABC, then AD is hypotenuse of ACD. Now you have a bunch of triangles that you can prove are equivilant and from there you can draw conclusions about the lengths of their sides.
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Bibliophile the BibleGuru
 
  1  
Reply Tue 25 Jan, 2005 01:55 pm
Good work, Engineer.
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vetrone
 
  1  
Reply Tue 25 Jan, 2005 02:40 pm
haha i sit behind you in class
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Linxflare
 
  1  
Reply Tue 25 Jan, 2005 08:37 pm
Haha ... i also sit beside you !!!
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El-Diablo
 
  1  
Reply Tue 25 Jan, 2005 08:55 pm
wow...
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tex
 
  1  
Reply Tue 1 Feb, 2005 12:18 pm
A right triangle is half a rectangle
x^2 + y^2 = r^2

Mid point of the hypotenuse is equidistant from the end points by definition.
The bisectors cross and make 4 isosceles triangles. Symmetry requires the 4
half bisectors to be equal.
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mathman
 
  1  
Reply Mon 21 Feb, 2005 09:56 pm
Hello
Make sure to use the following chart to help you keep track of your prove:

statement and reasons
---------------------------------------

Also, make sure to draw what you are given and apply the proper theories and postulates.

Feliz
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