The Pythagorean Theorem – Practice Problems

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The Pythagorean Theorem is an important result which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of its other two sides; i.e. a2 + b2 = c2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

Pythagorean triples are triples (a,b,c) of numbers which satisfy the Pythagorean Theorem. Given three numbers, the Pythagorean Theorem can be used to see if it is possible for those numbers to make up the side lengths of a right triangle or not.

The Pythagorean Theorem can also be used to solve various problems involving right triangles, like finding the length of a ladder leaning on a wall given the height of the wall and the distance of the foot of the ladder to the base of that wall.

Understand and apply the Pythagorean Theorem.


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Exercises in this Practice Problem
Define the Pythagorean Theorem.
Determine if the side lengths are a Pythagorean triple.
Find the areas.
Decide if the ladder fits.
Identify the right triangles.
Identify the Pythagorean triples.