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Math Help - Indirect proof

  1. #1
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    Indirect proof

    PROVE THAT the bisector of an angle of a scalene triangle cannot be perpendicular to the opposite side..

    Can any one give the explanation or discussion about this problem since i was absent that time when this topic is being discuss. Please give me hint how to do this ? thanks
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by jam2011 View Post
    PROVE THAT the bisector of an angle of a scalene triangle cannot be perpendicular to the opposite side..

    Can any one give the explanation or discussion about this problem since i was absent that time when this topic is being discuss. Please give me hint how to do this ? thanks
    Perhaps you could start here: consider an isosceles triangle and a line bisecting the vertex angle. Is this line perpendicular to the base?

    -Dan
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  3. #3
    Junior Member Kaloda's Avatar
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    Proof:

    Let ABC be a scalene triangle and D be the foot of the bisector of angle A at BC. Suppose that BC is perpendicular to AD, then it follows that angle DAB and angle ADB are congruent to angle DAC and angle ADC, respectively. Since AD=AD by reflexive property, then triangle ABD is congruent to triangle ACD by ASA, and thus AC = AB by CPCTC. But by defn. of Scalene triangle, AC cannot be congruent to AB and therefore a contradiction follows and the supposition is false and the theorem is true!
    Last edited by Kaloda; February 18th 2011 at 02:55 AM.
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  4. #4
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    , then it follows that angle DAB and angle ADB are congruent to angle DAC and angle ADC, respectively.


    THEN WHAT REASON THUS :angle DAB and angle ADB are congruent to angle DAC and angle ADC..OR WHAT DEFINITION......
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