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Math Help - Proving Right-Angled/Right Angle Triangle Help

  1. #1
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    Proving Right-Angled/Right Angle Triangle Help

    Hello there,

    I'm new here so please do not be angered if I make something wrong or I annoy you somehow with my question but I have just been given this question I cannot solve myself.

    ABC is right-angled at A. Given that AD is perpendicular to BC, prove that:

    AB X AD = BD x AC

    Thank you for your enlightenment.
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  2. #2
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    Quote Originally Posted by Hyeper View Post
    Hello there,

    I'm new here so please do not be angered if I make something wrong or I annoy you somehow with my question but I have just been given this question I cannot solve myself.

    ABC is right-angled at A. Given that AD is perpendicular to BC, prove that:

    AB X AD = BD x AC

    Thank you for your enlightenment.
    1. Draw a sketch.

    2. You are dealing with 2 right triangles: \Delta ABC and \Delta DBA. Both triangles have a right angle and the angle at B in common, thus they are similar.

    3. Corresponding sides are proportional:

    \dfrac{\overline{AC}}{\overline{AB}} = \dfrac{\overline{AD}}{\overline{BD}}

    4. Multiply the equation by the two denominators.
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  3. #3
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    Quote Originally Posted by earboth View Post
    1. Draw a sketch.

    2. You are dealing with 2 right triangles: \Delta ABC and \Delta DBA. Both triangles have a right angle and the angle at B in common, thus they are similar.

    3. Corresponding sides are proportional:

    \dfrac{\overline{AC}}{\overline{AB}} = \dfrac{\overline{AD}}{\overline{BD}}

    4. Multiply the equation by the two denominators.
    Thank you so much for your help. It's just so simple but I failed to comprehend what the question want...

    Btw, is it okay if I ask another question in this same thread or I have to start a new thread?

    Thank You
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  4. #4
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    Quote Originally Posted by Hyeper View Post
    Thank you so much for your help. It's just so simple but I failed to comprehend what the question want...

    Btw, is it okay if I ask another question in this same thread or I have to start a new thread?

    Thank You
    You are welcome!

    Better start a new thread as it is demanded in the rules of the forum (which you have read thoroughly, of course! )
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