# Median in right triangle

• Sep 9th 2012, 08:04 PM
Tim28
Median in right triangle
Prove that in a right triangle, the median from the right angle equals half the hypotenuse.

If two angles of a triangle are equal, the opposite sides are equal, hence the triangle is isosceles.

But how do I prove that the angles are equal?
• Sep 9th 2012, 09:56 PM
kalyanram
Re: Median in right triangle
Quote:

Originally Posted by Tim28
Prove that in a right triangle, the median from the right angle equals half the hypotenuse.

Hint: See the figure attached. Can you relate AE and AD.

Quote:

Originally Posted by Tim28
If two angles of a triangle are equal, the opposite sides are equal, hence the triangle is isosceles. But how do I prove that the angles are equal?

Its given to you that the angles are equal you need to prove that the sides opposite to them are indeed equal. Hence conclude that the triangle is isosceles.
• Sep 10th 2012, 05:21 PM
bjhopper
Re: Median in right triangle
Quote:

Originally Posted by Tim28
Prove that in a right triangle, the median from the right angle equals half the hypotenuse.

If two angles of a triangle are equal, the opposite sides are equal, hence the triangle is isosceles.

But how do I prove that the angles are equal?

Look up the definition of median
• Sep 10th 2012, 07:46 PM
Soroban
Re: Median in right triangle
Hello, Tim28!

Quote:

Prove that in a right triangle, the median from the right angle equals half the hypotenuse.

Proof without words . . .

Code:

              * * *           *          *  C         *              o       *                *       *                  *     Ao - - - - * - - - - oB       *        O        *       *                *         *              *           *          *               * * *
$\text{Draw }AC,\,BC,\text{ and }OC.$

$\text{Got it?}$

Okay, there were some words,
but they were directions for sketching the diagram.
(I couldn't type those slanted lines.)