The Pythagorean Theorem is a geometric principle that shows how the three sides of a right triangle relate to one another. It states that in a right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse. Note: The hypotenuse is the side of the triangle directly across from the right angle. The legs are the two sides that contain (or touch) the right angle.

The Pythagorean Theorem is expressed as follows:

a² + b² = c² where ‘a’ and ‘b’ are the legs and ‘c’ is the hypotenuse.

Examples:

1.) Imagine a right triangle where the legs are equal to 3 inches and 4 inches. What is the length of the hypotenuse?

Using the Pythagorean theorem, we substitute 3 inches and 4 inches for ‘a’ and ‘b’ to get:
(3 in)² + (4in)² = c²
(3 in)(3 in) + (4in)(4in) = c²
9in² + 16in² = c²
25in² = c²
√25in² = √c²
±5in = c
Since the length of a side can’t be negative, the answer is 5 in.

2.) Imagine a right triangle where one leg is equal to 7 inches and the hypotenuse is equal to 15 inches. What is the length of the missing leg?

Using the Pythagorean theorem, we substitute 7 inches and 15 inches for ‘a’ and ‘c’ respectively to get:
(7 in)² + b² = (15in)²
(7 in)(7 in) + b² = (15in)(15in)
49in² + b² = 225in²
-49in²              -49in²
b² = 176in²
√b² = √176in²
b ≈ ±13.27 in
Since the length of a side can’t be negative, the answer is ~13.27 in (read ‘approximately 13.27 inches’)

The Pythagorean theorem is useful for many things outside of a geometry class. You’ll find it used frequently in computer programming, architecture, and building design. Even if you don’t choose one of these as a career path, the Pythagorean theorem can be used to make home repairs and projects easier for everyone!