Pythagoras Vierecke Übungsblatt Lösungen
Diagonale: d = a •√2
b) Rechteck:
Hypotenuse: d = √a² + b²
Kathete 1: a = √d² – b²
Kathete 2: b = √d² – a²
c) Raute:
Hypotenuse: a = √(e/2)² + (f/2)²
Kathete 1: e/2 = √a²- (f/2)²
Kathete 2: f/2 = √a² – (e/2)²
d) Parallelogramm
α < 90°:
Hilfsgröße m = √(b² – ha²)
Hypotenuse: e = √(a + m)² + ha²
Kathete 1: ha² = √e² – (a + m)²
Kathete 2: a + m = √e² – ha²
Hypotenuse: f = √(a – m)² + ha²
Kathete 1: ha² = √f² – (a – m)²
Kathete 2: a – m = √f² – ha²
α > 90°:
Hilfsgröße m = √(b² – ha²)
Hypotenuse: e = √(a – m)² + ha²
Kathete 1: ha² = √e² – (a – m)²
Kathete 2: a – m = √e² – ha²
Hypotenuse: f = √(a + m)² + ha²
Kathete 1: ha² = √f² + (a + m)²
Kathete 2: a + m = √f² + ha²
e) Deltoid
Hypotenuse: √(x² + (f/2)²)
Kathete 1: x = √(a² – (f/2)²)
Kathete 2: f/2 = √(a² – x²)
Hypotenuse: b = √(y² + (f/2)²)
Kathete 1: y = √(b² – (f/2)²)
Kathete 2: f/2 = √(b² – y²
f) Trapez:
Hypotenuse: d = √ (h² + x²)
Kathete 1: h = √ (d² – x²)
Kathete 2: x = √ (d² – h²)
Hypotenuse: b = √ (h² + y²)
Kathete 1: h = √ (b² – y²)
Kathete 2: y = √ (b² – h²)
Hypotenuse: e = √ (a – y)² + h²
Kathete 1: h = √ e² – (a – y)²
Kathete 2: a – y = √ (e² – h²)
Hypotenuse: f = √ (a – x)² + h²
Kathete 1: h = √ f² – (a – x)²
Kathete 2: a – x = √ (f² – h²)
g) gleichschenkliges Trapez:
Hypotenuse: x = √ (b² – h²)
Kathete 1: h = √ (b² – x²)
Kathete 2: b = √ (h² + x²)
Hypotenuse: e = √ (a – x)² + h²
Kathete 1: h = √ e² – (a – x)²
Kathete 2: a – x = √ (e² – h²)