a2=b2+cd, an Extended Pythagorean Formula.

Consider triangle I ABC i , with Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>B</mi><mi>C</mi><mo»=</mo><mi>A</mi><mi>B</mi></mrow></math> ht . In particular, the angle opposite the side a is right if, and only if, i Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mi>a</mi></mrow><mn>2</mn></msup><mo>=</mo><msup><mrow><mi>b</mi></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mi>c</mi></mrow><mn>2</mn></msup></mrow></math> ht . I Let i Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></mrow></math> ht I , with i Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>a</mi><mo»=</mo><mi>b</mi></mrow></math> ht I , be the lengths of the sides of a triangle. [Extracted from the article]