Properties of Plane Figures
This page provides a comprehensive overview of various plane figures and their properties, focusing on triangles and quadrilaterals. The information is presented visually with diagrams and formulas for easy understanding.
Right-angled Triangle
The page begins with a right-angled triangle, showcasing the Pythagorean theorem.
Definition: The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of squares of the other two sides (a and b).
Formula: a² + b² = c²
This formula is crucial for calculating the długości boków w trójkącie prostokątnym (lengths of sides in a right-angled triangle).
Highlight: The page also includes a formula for calculating the wysokość w trójkącie prostokątnym (height in a right-angled triangle): h = (a * b) / c
Equilateral Triangle
Next, the properties of an equilateral triangle are presented.
Formula: The height (h) of an equilateral triangle is given by h = a√3 / 2, where 'a' is the length of a side.
Example: The area (P) of an equilateral triangle can be calculated using P = a²√3 / 4
Square
The properties of a square are illustrated, emphasizing its equal sides and right angles.
Definition: A square is a regular quadrilateral with four equal sides and four right angles.
Formula: The area of a square is given by P = a², where 'a' is the length of a side.
Highlight: The diagonal of a square is represented as a√2, which is an important property when considering przekątne kwadratu (diagonals of a square).
Rectangle
The rectangle's properties are shown next to the square for comparison.
Formula: The area of a rectangle is calculated as P = a * b, where 'a' and 'b' are the lengths of the sides.
Rhombus
The rhombus is presented with its diagonals and area formula.
Vocabulary: A rhombus is a quadrilateral with four equal sides.
Formula: The area of a rhombus is given by P = (e * f) / 2, where 'e' and 'f' are the lengths of the diagonals.
Trapezoid
The trapezoid (or trapezium) is shown with its area formula.
Formula: The wzór na pole trapezu (formula for the area of a trapezoid) is P = (a + b) * h / 2, where 'a' and 'b' are the lengths of the parallel sides and 'h' is the height.
Parallelogram
Finally, the parallelogram is presented with its area formula and angle relationships.
Formula: The area of a parallelogram is calculated as P = a * h, where 'a' is the base and 'h' is the height.
Highlight: The angles in a parallelogram have the following relationships: α + β = 180° and β + γ = 180°
This comprehensive guide serves as an excellent resource for students studying geometry, providing key formulas and visual representations for various plane figures.
