Final answer:
The Pythagorean Theorem is a fundamental principle in geometry that relates the sides of a right-angled triangle. It has applications in finding unknown side lengths and determining if a triangle is right-angled.
Step-by-step explanation:
The Pythagorean Theorem is a fundamental principle in geometry that establishes a relationship between the sides of a right-angled triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Mathematically, it can be expressed as a² + b² = c², where 'a' and 'b' are the lengths of the legs of the triangle and 'c' is the length of the hypotenuse.
The Pythagorean Theorem has numerous applications in geometry and real-world situations. One of its main applications is finding the length of an unknown side in a right triangle. For example, if the lengths of two sides (a and b) are known, we can use the theorem to find the length of the third side (c).
Another application is determining whether a triangle is right-angled or not. By applying the Pythagorean Theorem, we can check if the sum of the squares of the two shorter sides is equal to the square of the longest side. If it is, then the triangle is right-angled.