📚 Practice With Worksheets
Extend your learning by applying the Pythagorean Theorem to right triangles, assessments, quizzes, and real-world problem-solving situations.
▶️ Learn With Videos
Watch the related lessons to review finding exact answers in simplest radical form and applying the Pythagorean Theorem to solve problems.
🛠️ How to Use This Tool
Use this interactive visualizer to explore the Pythagorean Theorem. Adjust the sliders for leg \(a\) and leg \(b\), then watch how the right triangle and the attached squares change.
The squares on the two legs show \(a^2\) and \(b^2\). The square on the hypotenuse shows \(c^2\). As the side lengths change, compare the areas of the squares.
This tool works well for showing why the relationship \(a^2 + b^2 = c^2\) is true for right triangles.
🧠 Things to Think About
What happens to the hypotenuse when one leg gets longer? What happens to the area of the square attached to that side?
Why does \(3^2 + 4^2 = 5^2\)? How do the square areas help explain the relationship?
Does the equation \(a^2 + b^2 = c^2\) work for every triangle, or only for right triangles?
📘 Vocabulary
Pythagorean Theorem: In a right triangle, \(a^2 + b^2 = c^2\).
Right Triangle: A triangle that has one \(90^\circ\) angle.
Legs: The two sides that form the right angle. They are usually labeled \(a\) and \(b\).
Hypotenuse: The longest side of a right triangle. It is across from the right angle and is usually labeled \(c\).
Squared: Multiplying a number by itself. For example, \(4^2 = 4 \times 4 = 16\).
Square Area: The area of a square is found by multiplying side length by side length.
\(a^2\): The area of the square built on leg \(a\).
\(b^2\): The area of the square built on leg \(b\).
\(c^2\): The area of the square built on the hypotenuse.
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