Pythagoras’s Theorem
Pythagoras’s Theorem
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➢ Construct a right triangle.
➢ Use the select tool and click on each of the sides of the triangle.
➢ Choose length from the measure menu.
➢ Measures of each of the sides will appear in the upper left corner of the drawing canvass.
➢ We want to use the Sketchpad calculator to show the Pythagorean Theorem.
➢ Choose calculate from the measure menu to get the Sketchpad calculator.
➢ Click on the measure of one of the legs and it shows up in the calculator window. To square it click on the calculator keyboard ^2. Then click + and click on the measure of the other leg and square it. Press ok.
➢ Choose calculate from the measure menu to get the calculator again.
➢ Click on the measure of the hypotenuse and square it. Click ok.
➢ The two calculated values are the same. So for this triangle, leg squared plus leg squared equals hypotenuse squared.
➢ Use the select tool and drag any vertex or any side to change the shape of the right triangle. It remains a right triangle and the calculated values remain equal!
➢ “The proof is in the drag.”
The Pythagorean Theorem states that the sum of the squares of the legs of a right triangle equals the square of the hypotenuse.
a2 + b2 = c2
a
b
c
For another look at a proof of the Pythagorean Theorem go to
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Office for Mathematics, Science and Technology Education
mste.uiuc.edu
Office for Mathematics, Science and Technology Education
mste.uiuc.edu
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