# Pythagorean Theorem

## Applying the Pythagorean Theorem

Icon: In this video, learn how using the Pythagorean theorem can help people solve real-world problems involving distances. In the accompanying classroom activity, students develop their problem-solving, spatial reasoning, and geometry skills by putting the Pythagorean theorem to use. After a brief discussion about how to use the theorem to find the distance between two points on a coordinate grid, students partner up and play a game in which they generate (and then calculate the distance between) two or more points on the grid. As the game increases in complexity, students begin working in all quadrants and begin identifying multiple triangles that they can use to determine the distance between points.

## Applying the Pythagorean Theorem

Icon: In this video, watch an animated demonstration of using the Pythagorean theorem to find an unknown side of a right triangle. In the accompanying classroom activity, students solve problems in which they apply the Pythagorean theorem to find the sides of right triangles and to determine whether a set of triangle sides form a right triangle. To get the most from this lesson, students should be comfortable using a calculator to find square roots. They should also have experience solving equations involving an unknown square.

## Understanding the Pythagorean Theorem

Icon: In this video, learn how to use the Pythagorean theorem to find distance between two points on a coordinate grid. In the accompanying classroom activity, students apply what they learned in the video as they solve similar problems and discuss solution strategies. To get the most from this lesson, students should be comfortable using the Pythagorean theorem to find an unknown side of a right triangle, graphing points on the coordinate plane, and finding the distance between points with the same x- or y- values.

## Garfield'S Proof of the Pythagorean Theorem

Icon: This module explains a proof of the Pythagorean Theorem developed by James Garfield, the twentieth president of the United States.

## The Pythagorean Theorem Word Problem: Fishing Boat

Icon: This word problem asks you to use the Pythagorean Theorem to calculate that length of the rope that attaches the mast of a fishing boat to its deck.

## Special Right Triangles: 30-60-90 Triangle Side Ratios Proof

Icon: Learn how to prove the ratios between the sides of a 30-60-90 triangle.

## Bhaskara's Proof of the Pythagorean Theorem

Icon: This module explains an elegant visual proof of the Pythagorean Theorem developed by the 12th century Indian mathematician Bhaskara.

## Pythagorean Theorem: Solving for Unknown Sides

Icon: This module demonstrates how to use the Pythagorean Theorem to solve for an unknown side of a right triangle.

## The Pythagorean Theorem: the Width of a Rectangular Carpet

Icon: Use the Pythagorean Theorem to find the width of a rectangular carpet by dividing it into right triangles and solving for an unknown side.

## Special Right Triangles: 30-60-90 Triangle Example Problem

Icon: Using what we know about 30-60-90 triangles to solve what at first seems to be a challenging problem.