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Math Help - Isosceles Triangle ABC

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    Isosceles Triangle ABC

    Given: Isosceles triangle ABC with segment AB congruent to segment AC, and line CD is perpendicular to AB.

    Prove: Segment BC multiplied by segment BC is equal to two times Segment AB multiplied by Segment BD.

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  2. #2
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    Hello sologuitar
    Quote Originally Posted by sologuitar View Post
    Given: Isosceles triangle ABC with segment AB congruent to segment AC, and line CD is perpendicular to AB.

    Prove: Segment BC multiplied by segment BC is equal to two times Segment AB multiplied by Segment BD.

    Using Pythagoras' Theorem on \triangle ADC:
    DC^2=AC^2-AD^2
    = AB^2 -AD^2, since AC = AB (given)

    =(AB+AD)(AB-AD)

    =(AB+AD)(BD) ... (1)
    And using Pythagoras' Theorem on \triangle BDC:
    BC^2 = BD^2+DC^2
    = BD^2 + (AB+AD)(BD), from (1)

    =BD(BD +AB+AD)

    =BD(AB+AB)

    =2BD.AB
    Grandad
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