Understanding the Pythagorean Theorem
The Teorema di Pitagora, also known as the Pythagorean Theorem, is a cornerstone of geometry, particularly for right-angled triangles. This page provides a comprehensive overview of the theorem, its components, and its formulas.
The diagram on the page illustrates a right-angled triangle with its components clearly labeled. The sides of the triangle are identified as follows:
- C₁: cateto 1 firstcathetus
- C₂: cateto 2 secondcathetus
- i: ipotenusa hypotenuse
Definition: The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides catheti.
Highlight: The theorem is expressed mathematically as: A₁ + A₂ = A₃, where A₁ and A₂ represent the areas of squares constructed on the catheti, and A₃ represents the area of the square constructed on the hypotenuse.
The page presents several formulas derived from the Pythagorean Theorem:
- C₁² + C₂² = i²
- i = √C12+C22
- C₁ = √i2−C22
- C₂ = √i2−C12
Example: To find the length of the hypotenuse when C₁ = 3 and C₂ = 4, you would use the formula i = √32+42 = √9+16 = √25 = 5.
The page also includes additional geometric formulas related to the right-angled triangle:
- Area of the triangle: A = C1×C2 / 2
- Height of the triangle: h = C1×C2 / i
Vocabulary:
- Cateto: In Italian, this refers to one of the sides adjacent to the right angle in a right-angled triangle.
- Ipotenusa: The Italian term for hypotenuse, which is the longest side of a right-angled triangle, opposite the right angle.
This comprehensive presentation of the Teorema di Pitagora provides students with a spiegazione semplice simpleexplanation of this fundamental geometric principle, making it an excellent resource for scuola media middleschool students studying geometry.