Understanding the Pythagorean Theorem: Identifying right triangles and their characteristics

Regarding side length, a triangle is a right triangle if …

A triangle is considered a right triangle if it satisfies the Pythagorean theorem, which states that in a right triangle, the square of the length of the longest side (called the hypotenuse) is equal to the sum of the squares of the lengths of the other two sides

A triangle is considered a right triangle if it satisfies the Pythagorean theorem, which states that in a right triangle, the square of the length of the longest side (called the hypotenuse) is equal to the sum of the squares of the lengths of the other two sides.

In other words, if a, b, and c represent the lengths of the sides of a triangle, with c being the hypotenuse, then the Pythagorean theorem can be stated as:

a^2 + b^2 = c^2

This means that in a right triangle, the square of the length of one side plus the square of the length of the other side is equal to the square of the length of the hypotenuse.

For example, let’s say we have a triangle with side lengths of 3 cm, 4 cm, and 5 cm. We can see that:

3^2 + 4^2 = 9 + 16 = 25

And 5^2 = 25

Since the sum of the squares of the two shorter sides is equal to the square of the longest side, this triangle satisfies the Pythagorean theorem, making it a right triangle.

It is important to note that the Pythagorean theorem only applies to right triangles. If the equation a^2 + b^2 = c^2 does not hold, then the triangle is not a right triangle.

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