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The Pythagorean Theorem
Concept sheet | Mathematics
The Pythagorean Theorem (also called the Pythagorean relationship) applies only to right triangles. The theorem is used to find the measure of one side when the measures of the other two sides are known.
Secondary
3
Table of contents
The legs of a right triangle, often denoted |a| and |b,| correspond to the 2 sides that form the right angle.
The hypotenuse of a right triangle, denoted |c,| is the longest side. In other words, the hypotenuse is the side that is opposite the right angle.
The Pythagorean Theorem is stated as follows:
In a right triangle, the sum of the measures of the legs squared is equal to the measure of the hypotenuse squared.||a^2+b^2=c^2||
The Pythagorean Theorem can be represented using variables other than |a,| |b| and |c.| For example, the equation |x^2+y^2=z^2| is equally valid as the equation |a^2+b^2=c^2.|
Examples
Here are some examples of how to apply the Pythagorean Theorem.
The Pythagorean Theorem can also be used to verify if a triangle is right-angled or not. A triangle is right-angled if and only if it satisfies the Pythagorean Theorem.
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If the relationship |a^2+b^2=c^2| is true, the triangle is right-angled.
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If the relationship |a^2+b^2=c^2| is false, the triangle is not right-angled.