Geometric Formulas and Mathematical Relationships

This comprehensive page details essential geometric formulas and mathematical relationships used in plane geometry. The content focuses on triangles, quadrilaterals, and their properties.

Definition: The Pythagorean theorem states that in a right triangle, a² + b² = c², where c is the hypotenuse and a and b are the other two sides.

Example: In a 30-60-90 triangle, the relationships between angles follow the pattern: 30° + 60° + 90° = 180°

Highlight: The diagonal of a square can be calculated using the formula d = a√2, where a is the side length of the square.

Vocabulary:

• Przekątna: diagonal
• Wysokość: height
• Trójkąt równoboczny: equilateral triangle

Quote: "Pole trójkąta równobocznego P = a²√3/4" (Area of an equilateral triangle)

The page includes several key mathematical concepts:

• The height formula for an equilateral triangle: h = a√3/2
• The area formula for triangles: P = (a+b)·h/2
• Angle sum properties in triangles and quadrilaterals
• Coordinate geometry principles for calculating distances between points