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Math Help - Median in right triangle

  1. #1
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    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?
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  2. #2
    Member kalyanram's Avatar
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    Re: Median in right triangle

    Quote Originally Posted by Tim28 View Post
    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 View Post
    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.
    Attached Thumbnails Attached Thumbnails Median in right triangle-rttri.png  
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  3. #3
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    Re: Median in right triangle

    Quote Originally Posted by Tim28 View Post
    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
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  4. #4
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    Re: Median in right triangle

    Hello, Tim28!

    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.)
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