Regarding side length, a triangle is a right triangle if …
A triangle is considered a right triangle if and only if it satisfies the Pythagorean Theorem, which states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides
A triangle is considered a right triangle if and only if it satisfies the Pythagorean Theorem, which states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In other words, if a triangle has sides of lengths a, b, and c, and if c is the longest side (the hypotenuse), then it is a right triangle if and only if a^2 + b^2 = c^2.
This theorem is named after the ancient Greek mathematician Pythagoras, who discovered and formulated it. Right triangles have been studied extensively and have various properties that make them important in mathematics and applied fields like engineering, architecture, and physics. The most famous example of a right triangle is the 3-4-5 triangle, where the sides have lengths of 3 units, 4 units, and 5 units, respectively.
To determine if a given triangle is a right triangle, you can use the Pythagorean Theorem. Simply square the lengths of the two shorter sides and check if the sum of their squares equals the square of the longest side. If it does, then the triangle is a right triangle.
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