Right-Angled Triangles

This page focuses on the properties and formulas related to right-angled triangles.

The wzór na pole trójkąta prostokątnego (formula for the area of a right-angled triangle) is presented in multiple forms:

1. P = (1/2)ab, where 'a' and 'b' are the lengths of the two perpendicular sides.
2. P = (1/2)ch, where 'c' is the hypotenuse and 'h' is the height to the hypotenuse.

The Pythagorean theorem is highlighted: a² + b² = c², where 'c' is the hypotenuse and 'a' and 'b' are the other two sides.

Definition: Altitude (wysokość) - The perpendicular line segment from a vertex to the opposite side (or its extension) in a triangle.

Example: The formula for the altitude of a right-angled triangle is given as h = (xy) / c, where 'x' and 'y' are segments of the hypotenuse created by the altitude.

Highlight: The diameter of the circumcircle of a right-angled triangle is equal to the length of its hypotenuse.

Scalene Triangles and General Triangle Properties

This page covers scalene triangles and general properties applicable to all triangles.

For scalene triangles, the wzór na pole trójkąta (formula for the area of a triangle) is presented in various forms:

1. P = (1/2)ah, where 'a' is any side and 'h' is the corresponding height.
2. P = (1/2)bc sin α, where 'b' and 'c' are two sides and α is the angle between them.

The page also discusses the classification of triangles based on their angles:

• Acute triangle: All angles < 90°
• Right-angled triangle: One angle = 90°
• Obtuse triangle: One angle > 90°

Vocabulary: Scalene triangle (trójkąt różnoboczny) - a triangle with no two sides of equal length.

Highlight: In an acute triangle, the center of the circumcircle lies inside the triangle, while in an obtuse triangle, it lies outside.