triangle: The median drawn to the hypotenuse of a right tria

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humakhan

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May 19, 2005
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prove the theorem given . what specifically do you need to prove in the figure?

The median drawn to the hypotenuse of a right triangle divides it into two isosceles triangles.

( i cant attach the picture here, but i'll tell you how it looks)
its a right triangle ABC and D divides the triangle into two. giving B and C which is the hypotenuse , equal.

BD = CD........given
anything else that we need to prove besides bd = cd ?

can we also say AD = CD and AB = DB ?

this would be much easier if i had a picture to show you. so you would know what i am talking about. ddoes anyone know what i am talking about?
 
We could attempt an algebraic proof.

I am guessing with no drawing. It would help if you could post your drawing instead of describing it. Remember the picture and thousand words thing?. :)

Let x be the segment from A to D. The line you drew to bisect the hypoteneuse.

Pythagoras:

\(\displaystyle a^{2}+b^{2}=c^{2}\)

\(\displaystyle x^{2}+(\frac{c}{2})^{2}=b^{2}=a^{2}\)

\(\displaystyle x^{2}+(\frac{c}{2})^{2}+x^{2}+(\frac{c}{2})^{2}=c^{2}\)

\(\displaystyle 2x^{2}+\frac{c^{2}}{2}=c^{2}\)

\(\displaystyle x=\frac{c}{2}\)

Therefore, x and c/2 are the equal and the triangles are isosceles.

trianglexs8.gif
 
Thanks so very much for the help
and yeah about the picture.. i dont know how to place it here.
from my computer to here...how you do that?
 
Is your picture a gif file, jpeg, etc?.

Go to this link: http://www.imageshack.us/

click on browse to find your file and then click 'host it'.

Give it a minute to load. You'll see a bunch of links appear. Go to the bottom one and copy and paste it into the forum with
on the other end.

Give it a go.
 
Re: triangle

humakhan said:
prove the theorem given . what specifically do you need to prove in the figure?

The median drawn to the hypotenuse of a right triangle divides it into two isosceles triangles.

( i cant attach the picture here, but i'll tell you how it looks)
its a right triangle ABC and D divides the triangle into two. giving B and C which is the hypotenuse , equal.

BD = CD........given
anything else that we need to prove besides bd = cd ?

can we also say AD = CD and AB = DB ?

this would be much easier if i had a picture to show you. so you would know what i am talking about. ddoes anyone know what i am talking about

Given triangle ABC, A the right angle.
AD bisects, the hypotenuse at D.
BD = CD
From D, draw perpendicular to AC, DE.
AE = CE
Therefore, AD = CD making triangle ADC isosceles.

The same procedure leads tro triangle ABD being isosceles.
Click to expand...
 
Re: triangle: The median drawn to the hypotenuse of a right

Hello, humakhan!

There is an "eyeball" proof for this one . . .

The median drawn to the hypotenuse of a right triangle divides it into two isosceles triangles.
Click to expand...

Right triangle \(\displaystyle ABC\) can be inscribed in a semicircle.
Code: 
         C    * * *
          o           *
        *  \ o          *
       * o  \   o        *
             \     o
      * o     \       o   *
      *        \          *
      o - - - - + - - - - o
      A         O         B

Hence: \(\displaystyle \,OA\,=\,OB\,=\,OC\) . . . They are radii.

Therefore, \(\displaystyle \Delta AOC\) and \(\displaystyle \Delta BOC\) are isosceles.

 
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