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# Revision 645679 of Proving the Pythagorean theorem

• Revision slug: Web/MathML/Examples/MathML_Pythagorean_Theorem
• Revision title: Proving the Pythagorean theorem
• Revision id: 645679
• Created:
• Creator: Tao
• Is current revision? Yes
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## Revision Content

We will now prove the Pythogorian theorem: ${a}^{2}+{b}^{2}={c}^{2}$

We can prove the theorem algebraically by showing that the area of the big square equals the area of the inner square (hypotenuse squared) plus the area of the four triangles: $( a + b ) 2 = c 2 + 4 ⋅ ( 1 2 a b ) a 2 + 2 a b + b 2 = c 2 + 2 a b a 2 + b 2 = c 2$

## Revision Source

```<p>We will now prove the Pythogorian theorem: [itex] <mrow> <msup><mi> a </mi><mn>2</mn></msup> <mo> + </mo> <msup><mi> b </mi><mn>2</mn></msup> <mo> = </mo> <msup><mi> c </mi><mn>2</mn></msup> </mrow> [/itex]</p>
<p>We can prove the theorem algebraically by showing that the area of the big square equals the area of the inner square (hypotenuse squared) plus the area of the four triangles: <math style="display: block;"> <mtable columnalign="right center left"> <mtr> <mtd> <msup> <mrow> <mo> ( </mo> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mtd> <mtd> <mo> = </mo> </mtd> <mtd> <msup><mi> c </mi><mn>2</mn></msup> <mo> + </mo> <mn> 4 </mn> <mo> ⋅ </mo> <mo>(</mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mi> a </mi><mi> b </mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <msup><mi> a </mi><mn>2</mn></msup> <mo> + </mo> <mn> 2 </mn><mi> a </mi><mi> b </mi> <mo> + </mo> <msup><mi> b </mi><mn>2</mn></msup> </mtd> <mtd> <mo> = </mo> </mtd> <mtd> <msup><mi> c </mi><mn>2</mn></msup> <mo> + </mo> <mn> 2 </mn><mi> a </mi><mi> b </mi> </mtd> </mtr> <mtr> <mtd> <msup><mi> a </mi><mn>2</mn></msup> <mo> + </mo> <msup><mi> b </mi><mn>2</mn></msup> </mtd> <mtd> <mo> = </mo> </mtd> <mtd> <msup><mi> c </mi><mn>2</mn></msup> </mtd> </mtr> </mtable> [/itex]</p>```