how can the Pythagoras theorem be proved by paper cutting pasting and folding?

Question

please metion the procedure

Answer 1

draw a right angle triangle. then draw 3 squares, each on a different side of the triangle and matching exactly the length of that side of the triangle, then cut the 3 squares and try and cover the large square with cuts from the 2 other squares, according to the Pythagoras theorem the areas of the 2 smaller squares will match exactly the area of the largest square.

Answer 2

Cut three squares, 3 x 3, 4 x 4, 5 x 5, and draw a 1" grid on each one. Then make a right triangle, placing the 4" and 3" at 90 degrees to each other. The 5" is the hypotenuse. this demonstrates it beautifully (9 +16 = 25)

Answer 3

i agree with Scummibea

Phthagorean Theorem

c² = a² + b²

30- 60 - 90 Triangle

cut nine pieces of paper

3 x 3 = 9

cut sixteen pieces of paper

4 x 4 = 16

Cut 25 pieces of paper

5 x 5 = 25

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Let

3 x 3 pieces of paper equal the adjacent side

4 x 4 pieces of paper equal the opposite side

5 x 5 pieces of paper equal the hypotenuse

Draw a right triangle and insert the pieces of paper

Click on the URL below for additional information concernint Pythagorean Theorem

www.pbs.org/wgbh/nova/proof/puzzle/theorem.html



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Answer 4

i guess if you use the Pythagorean Theorem to solve for the length of the hypotenuse, for example, with sides measuring 3 inches and 4 inches, youd come up with a hypotenuse of 5 inches, right?

draw a right triangle with sides of 3 inches and 4 inches. use a ruler to draw a straight line for the hypotenuse. cut out the triangle. if you used a ruler to measure the hypotenuse, it should be 5 inches, proving your formula works.

you could do this on a larger scale with a 6-8-10 right triangle.

as for pasting and folding, i have no clue.

Answer 5

try the given link its got 72 proofs for the theorem 2-3 of them may intrest you