{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/b\/b4\/Do-Garfield%27s-Proof-of-the-Pythagorean-Theorem-Step-2.jpg\/v4-460px-Do-Garfield%27s-Proof-of-the-Pythagorean-Theorem-Step-2.jpg","bigUrl":"\/images\/thumb\/b\/b4\/Do-Garfield%27s-Proof-of-the-Pythagorean-Theorem-Step-2.jpg\/aid2777359-v4-728px-Do-Garfield%27s-Proof-of-the-Pythagorean-Theorem-Step-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>

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<\/p><\/div>"} 2 Construct a similar triangle with side b now extending in a straight line from the original side a, then with side a parallel along the top to the bottom original side b, and side c connecting the endpoints of the new a and b.

{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/e\/e9\/Do-Garfield%27s-Proof-of-the-Pythagorean-Theorem-Step-3.jpg\/v4-460px-Do-Garfield%27s-Proof-of-the-Pythagorean-Theorem-Step-3.jpg","bigUrl":"\/images\/thumb\/e\/e9\/Do-Garfield%27s-Proof-of-the-Pythagorean-Theorem-Step-3.jpg\/aid2777359-v4-728px-Do-Garfield%27s-Proof-of-the-Pythagorean-Theorem-Step-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>

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<\/p><\/div>"} 3 Understand the goal. We are interested to know the angle x formed where the two side c's meet. Thinking about it, the original triangle was made of 180 degrees with the angle on the right at the far end of b, called theta, and the other angle at the top of a, being 90 degrees minus theta, as all the angles total 180 degrees and we already have one 90 degree angle.

{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/a\/a6\/Do-Garfield%27s-Proof-of-the-Pythagorean-Theorem-Step-4.jpg\/v4-460px-Do-Garfield%27s-Proof-of-the-Pythagorean-Theorem-Step-4.jpg","bigUrl":"\/images\/thumb\/a\/a6\/Do-Garfield%27s-Proof-of-the-Pythagorean-Theorem-Step-4.jpg\/aid2777359-v4-728px-Do-Garfield%27s-Proof-of-the-Pythagorean-Theorem-Step-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>

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<\/p><\/div>"} 4 Transfer your angle knowledge to the upper new triangle. At the bottom, we have theta, at the top left we have 90 degrees, and the top right we have 90 degrees minus theta. The mystery angle x is 180 degrees. So theta + 90 degrees-theta + x = 180 degrees. Adding theta and negative theta gives us zero on the left, and subtracting 90 degrees from both sides leaves x equal to 90 degrees. So we have established that the mystery angle x = 90 degrees. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/e\/e8\/Do-Garfield%27s-Proof-of-the-Pythagorean-Theorem-Step-4Bullet1.jpg\/v4-460px-Do-Garfield%27s-Proof-of-the-Pythagorean-Theorem-Step-4Bullet1.jpg","bigUrl":"\/images\/thumb\/e\/e8\/Do-Garfield%27s-Proof-of-the-Pythagorean-Theorem-Step-4Bullet1.jpg\/aid2777359-v4-728px-Do-Garfield%27s-Proof-of-the-Pythagorean-Theorem-Step-4Bullet1.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>

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<\/p><\/div>"} At the bottom, we have theta, at the top left we have 90 degrees, and the top right we have 90 degrees minus theta.

{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/e\/e8\/Do-Garfield%27s-Proof-of-the-Pythagorean-Theorem-Step-5.jpg\/v4-460px-Do-Garfield%27s-Proof-of-the-Pythagorean-Theorem-Step-5.jpg","bigUrl":"\/images\/thumb\/e\/e8\/Do-Garfield%27s-Proof-of-the-Pythagorean-Theorem-Step-5.jpg\/aid2777359-v4-728px-Do-Garfield%27s-Proof-of-the-Pythagorean-Theorem-Step-5.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>

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<\/p><\/div>"} 5 Look at the whole figure as a trapezoid in two ways. First, the formula for a trapezoid is A= the Height x (Base1 + Base 2)/2. The height is a+b and (Base1 + Base 2)/2 = 1/2(a + b). So that all equals 1/2 (a+b)^2.