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In geometry, the inverse Pythagorean theorem (also known as the reciprocal Pythagorean theorem or the upside down Pythagorean theorem) is as follows: Let A, B be the endpoints of the hypotenuse of a right triangle ABC. Let D be the foot of a perpendicular dropped from C, the vertex of the right angle, to the hypotenuse. Then

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  • Inverser Satz des Pythagoras (de)
  • Inverse Pythagorean theorem (en)
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  • Der Inverse Satz des Pythagoras besagt in der euklidischen Geometrie, dass in allen ebenen rechtwinkligen Dreiecken die Summe aus den inversen Katheten­quadraten gleich dem inversen Höhen­quadrat über der Hypotenuse ist. Wenn a und b die Längen der Katheten sind, die in der gemeinsamen Ecke C den rechten Winkel einschließen, und h die Höhe von C über der Hypotenuse ist, siehe Bild, dann bedeutet das: Anders als im Satz des Pythagoras „a2+b2=c2“ werden hier die Inversen der Kathetenquadrate addiert, was den Namen motiviert. (de)
  • In geometry, the inverse Pythagorean theorem (also known as the reciprocal Pythagorean theorem or the upside down Pythagorean theorem) is as follows: Let A, B be the endpoints of the hypotenuse of a right triangle ABC. Let D be the foot of a perpendicular dropped from C, the vertex of the right angle, to the hypotenuse. Then (en)
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  • Der Inverse Satz des Pythagoras besagt in der euklidischen Geometrie, dass in allen ebenen rechtwinkligen Dreiecken die Summe aus den inversen Katheten­quadraten gleich dem inversen Höhen­quadrat über der Hypotenuse ist. Wenn a und b die Längen der Katheten sind, die in der gemeinsamen Ecke C den rechten Winkel einschließen, und h die Höhe von C über der Hypotenuse ist, siehe Bild, dann bedeutet das: Anders als im Satz des Pythagoras „a2+b2=c2“ werden hier die Inversen der Kathetenquadrate addiert, was den Namen motiviert. (de)
  • In geometry, the inverse Pythagorean theorem (also known as the reciprocal Pythagorean theorem or the upside down Pythagorean theorem) is as follows: Let A, B be the endpoints of the hypotenuse of a right triangle ABC. Let D be the foot of a perpendicular dropped from C, the vertex of the right angle, to the hypotenuse. Then This theorem should not be confused with proposition 48 in book 1 of Euclid's Elements, the converse of the Pythagorean theorem, which states that if the square on one side of a triangle is equal to the sum of the squares on the other two sides then the other two sides contain a right angle. (en)
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