# Thread: hypotenuse of a right triangle

1. ## hypotenuse of a right triangle

Hi,

I need help with this problem. May someone help me please?

The Problem is: You are asked to prove the theorem given below, using the figure shown. 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.

2. Thou art asked to show that,

Use the following theorem.
Theorem: Given a triangle ABC. From A draw a median to BC. Let is intersect at D.
Then,

Now the triangle which we have is right.
Hence,
AB^2+AC^2 = BC^2 by Pythagorean Theorem.

Thus,
But (1/2)BC=BD=DC
Hence,
Hence the two triangles are isoseles.
Q.E.D.

3. Hello, JayJay!

Prove: the median drawn to the hypotenuse of a right triangle
divides it into two isosceles triangles.
There is an "eyeball" proof for this.
Maybe you can explain it in words.

Code:
                * * *      C
*               o
*             o    o*
*          o         o*
o              o
*   o                   *
A o   o   o   *   o   o   o B
*     r     O     r     *

*                     *
*                   *
*               *
* * *

A right triangle can be inscribed in a semicircle.

We have right triangle ABC inscribed in a semicircle with radius r.
. . Hence: OA = OB = r.

Draw radius OC and we have:
. . OC = OA . . ∆AOC is isosceles.
. . OC = OB . . ∆COB is isosceles.

4. Thank you