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Math Help - Help! - Pythagorean Theorem Proof

  1. #1
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    Smile Help! - Pythagorean Theorem Proof

    In need of help. I've searched the internet and can't seem to find a pythag proof that makes since to me.

    Looking at the diagram below and using the following theorem, how do you prove the pythagorean theorem.

    Theorem: The power of a point is well defined; that is, the same value is obtained regardless of which line l is used in the definition as long as the line has at least one point of intersection with the circle.

    I'd even settle for just proving the pythagorean theorem without using the above theorem.

    Prove: (AD)(DC) = (AE)(EB) + (BF)(FC)


    Help! - Pythagorean Theorem Proof-pythag-theorem.jpg
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  2. #2
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    Quote Originally Posted by ReneePatt View Post
    In need of help. I've searched the internet and can't seem to find a pythag proof that makes since to me.

    Looking at the diagram below and using the following theorem, how do you prove the pythagorean theorem.

    Theorem: The power of a point is well defined; that is, the same value is obtained regardless of which line l is used in the definition as long as the line has at least one point of intersection with the circle.

    I'd even settle for just proving the pythagorean theorem without using the above theorem.

    Prove: (AD)(DC) = (AE)(EB) + (BF)(FC)


    Click image for larger version. 

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    HI

    Take a look at the diagram i attached . \triangle ABC with right angle at B . Then construct BD which is perpendicular to AC . We are trying to prove that AC^2=AB^2+BC^2

    so here \triangle ADB , \triangle ABC , \triangle BDC are similar .

    \frac{AD}{AB}=\frac{AB}{AC}\Rightarrow AB^2=AD\cdot AC

    \frac{BD}{DC}=\frac{AC}{BC}\Rightarrow BC^2=AC\cdot DC

    \therefore AB^2+BC^2=AD\cdot AC+AC\cdot DC=AC(AD+DC)=AC\cdot AC

    hence proved .
    Attached Thumbnails Attached Thumbnails Help! - Pythagorean Theorem Proof-phythogoras.bmp  
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  3. #3
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    Quote Originally Posted by mathaddict View Post

    so here \triangle ADB , \triangle ABC , \triangle BDC are similar .
    Hi,
    You say that \triangle ADB , \triangle ABC , \triangle BDC are similar but there isn't a \triangle BDC. Did you mean \triangle ADC?
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  4. #4
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    Quote Originally Posted by ReneePatt View Post
    Hi,
    You say that \triangle ADB , \triangle ABC , \triangle BDC are similar but there isn't a \triangle BDC. Did you mean \triangle ADC?
    hey the diagram i attached previously is incorrect . This is the correct one . I accidentally swapped the A and B .
    Attached Thumbnails Attached Thumbnails Help! - Pythagorean Theorem Proof-phy.bmp  
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  5. #5
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    Smile

    Quote Originally Posted by mathaddict View Post
    hey the diagram i attached previously is incorrect . This is the correct one . I accidentally swapped the A and B .

    Thank you very much!!

    This makes so much sense.
    Last edited by ReneePatt; December 11th 2009 at 07:50 AM. Reason: Added more
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