The Pythagorean theorem

In short: In a right-angled triangle a² + b² = c². The hypotenuse c is the longest side and lies opposite the right angle; a and b are the legs.

In more detail: With the theorem a missing side can be calculated when two sides are known.

In detail

• Example: Legs 3 and 4: c² = 9 + 16 = 25, so c = 5.
• Calculating a leg: a² = c² − b².
• Converse: If a² + b² = c², the triangle is right-angled.
• Pythagorean triples: 3-4-5, 5-12-13, 8-15-17.
• Application: Diagonal of a rectangle, ladder against a wall, distance between two points.
• Craftsman’s trick: Set out right angles with a 3-4-5 cord.
• Extension: Trigonometry for arbitrary angles (trigonometrie-sinus-kosinus-tangens).
• Areas: Calculate triangles and areas (geometrie-flaechen-und-koerper-formeln).