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Which of the images above represents a proof of the Pythagorean Theorem? Explain your choice, and then explain how the figure proves the Pythagorean Theorem.

  • Math -

    http://www.google.com/search?q=proof+of+the+pythagorean+theorem&hl=en&tbo=u&tbm=isch&source=univ&sa=X&ei=6l6qUOnIG6PvygG3yIGICw&sqi=2&ved=0CD4QsAQ&biw=711&bih=453

  • Math -

    sorry i don't see a picture. But, I'll explain what should be seen. Make a right triangle. From the angle <B, where B is 90 degrees, draw an altitude down to CA. Call that point D. We see that ABC and BCD are similar triangles. BC/CD=AC/BC, so BC^2=AC*CD. Likewise, ADB is similar to ABC, so we get AB/AD=AC/AB, so AB^2=AD*AC.So we add these equations together for BC^2 and AB^2, to get AC*CD + AD*AC = AC(CD+AD) = AC^2 Thus, a^2 + b^2 = c^2 in a right triangle.

  • Math -

    BTW, A would be at the top if the right triangle were standing on its shorter base. C would be on the other side on the bottom right. B would be on the right angle

  • Math -

    OMG WHAT THE ANSWER!!!!!!!!!!!!!!!!!!!!!!

  • Math -

    Figure B proves the Pythagorean Theorem.
    As you may have noticed, the lengths given for both figures are already perfect squares. All you have to do is add the lengths of the legs to see if they equal the length of the hypotenuse/diagonal.
    Figure A: 9 + 36 = 46... not 64
    Figure B: 25 + 144 = 169... correct
    Figure B proves the Pythagorean Theorem.
    Pythagorean Theorem Formula: a^2 + b^2 = c^2
    (The numbers are already squared, so just plug them in for a, b, and c, and see if it is a true statement.)

    Hope this helps and I hope it made sense.

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