geometry

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Prove that median of a isoeceles trinangle is perpendicular to the unequal sides.

  • geometry -

    given:
    ABC is an isosceles triangle with
    AB = AC ---- by definition
    If AD is the median to BC
    BD = CD ---- given
    AD = AD --- common side
    therefore triangle ABD is congruent to triangle ACD (SSS)
    Therefore angle ADB = angle ADC
    but angle ADB + ADC = 180
    so each angle = 90°

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