Introduction to the Pythagorean Theorem Notes
The Pythagorean Theorem is a formula for right triangles. In the real world, it was used in the construction of the Parthenon. We’ll discover additional uses as we work through the chapter.
The Pythagorean Theorem deals ONLY with Right Triangles. You cannot assume that a triangle is a right triangle by looking at it. Right triangles are indicated by a box in one of the angles OR by a 90° marking.
Right triangle with box and 90 degree indicators
The side across from the 90° angle is called the hypotenuse. It is always the longest side. The other two sides are called legs.
Right triangle with a box in the lower right corner indicating a right angle;
Image used via creative commons license from: http://go.osu.edu/CzCn
In the Pythagorean Theorem the legs are referred to as A and B. The hypotenuse is referred to as C.
The Pythagorean Theorem is used to find the length of one of the legs or the hypotenuse. You may also determine if a triangle is a right triangle by plugging its side lengths into the formula and solving. If it creates a solution, it is a right triangle.
The formula is: a2 + b2 = c2
In the “real world” one application might be to find the height of a ladder leaned against a house. The house makes a right angle with the ground, where the ladder makes up the hypotenuse.
Ladder leaning on house
For additional explanations, watch the following videos:
The first video provided visual explanations of right triangles and their parts, as well as the Pythagorean Theorem. It also has example problems and extra practice. It is a good idea to watch through to the end if you’re wondering where this theorem came from!
The second video breaks down where the Pythagorean Theorem came from. It provides pictures showing why each side gets squared when using the formula. In addition, there are examples and worked problems throughout the video.
The third video is more of a fun application video. It gives you the basic definitions of right triangles and their parts. The main part of the video is using the Pythagorean Theorem to solve a “real life” (in the case of the main character) problem.