Properties of Rectangles, Triangles, and Trapezoids

This page expands on Figury na płaszczyźnie teoria by covering the properties of rectangles, triangles, and trapezoids.

Rectangle properties:

• Sum of interior angles: 360°
• Area formula: A * B (length times width)
• Diagonal length: D = √(A² + B²)
• Perimeter formula: 2A + 2B

Triangle properties:

• Sum of interior angles: 180°
• Area formula: 1/2 * base * height

Trapezoid properties:

• Sum of interior angles: 360°
• Area formula: (a + b) * h / 2, where a and b are parallel sides and h is the height

Definition: A trapezoid is a quadrilateral with at least one pair of parallel sides.

Highlight: The formula for a rectangle's diagonal, D = √(A² + B²), is derived from the Pythagorean theorem, showcasing the interconnectedness of geometric concepts.

These properties form the basis for more advanced topics in Geometria płaska WZORY and are essential for solving problems in Geometria płaska zadania.

Advanced Angles and Square Properties

This section continues with more complex angles and introduces the properties of a square, which is fundamental in Figury geometryczne na płaszczyźnie.

Additional angle types are presented:

• Reflex angle (Kąt wklęsły): Measures between 180° and 360°
• Full angle (Kąt pełny): Exactly 360°
• Adjacent angles (Kąty przyległe): Two angles that share a common side and vertex

The properties of a square are then detailed:

• Sum of interior angles: 360°
• Area formula: A² = A * A, where A is the side length
• Diagonal length: D = A√2
• Perimeter formula: 4A

Vocabulary: Adjacent angles are two angles that share a common vertex and one common side, but do not overlap.

Example: In a square with a side length of 5 units, the area would be 25 square units (5² = 5 * 5 = 25), and the perimeter would be 20 units (4 * 5 = 20).