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In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
- The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).
- Theorem
- Find the length of the hypotenuse. Our goal is to solve for the length of the hypotenuse. We are given the lengths of the two legs. We know two sides out of the three!
- Find the length of the leg. Just by looking at the figure above, we know that we have enough information to solve for the missing side. The reason is the measure of the two sides are given and the other leg is left as unknown.
- Do the sides [latex]17[/latex], [latex]15[/latex] and [latex]8[/latex] form a right triangle? If so, which sides are the legs and the hypotenuse?
- A rectangle has a length of [latex]8[/latex] meters and a width of [latex]6[/latex] meters. What is the length of the diagonal of the rectangle?
May 10, 2024 · Recent News. Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2. Although the theorem has long been associated with Greek mathematician-philosopher ...
- The Editors of Encyclopaedia Britannica
Learn how to use and prove the Pythagorean theorem, which describes the relationship between the sides of a right triangle. Explore examples, word problems, distance formula and proofs with interactive exercises and quizzes.
5 days ago · Pythagorean Theorem. Download Wolfram Notebook. For a right triangle with legs and and hypotenuse , (1) Many different proofs exist for this most fundamental of all geometric theorems. The theorem can also be generalized from a plane triangle to a trirectangular tetrahedron, in which case it is known as de Gua's theorem. The various proofs of ...
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It is called "Pythagoras' Theorem" and can be written in one short equation: a 2 + b 2 = c 2. Note: c is the longest side of the triangle; a and b are the other two sides; Definition. The longest side of the triangle is called the "hypotenuse", so the formal definition is:
The Pythagorean theorem or Pythagoras’s theorem is a statement about the sides of a right triangle. One of the angles of a right triangle is always equal to 90 90 degrees. This angle is the right angle. The two sides next to the right angle are called the legs and the other side is called the hypotenuse. The hypotenuse is the side opposite ...
