# Lesson 10

Applications of the Pythagorean Theorem

### Lesson Narrative

In this lesson students use the Pythagorean Theorem and its converse as a tool to solve application problems. In the first activity, they solve a problem involving the distance and speed of two children walking and riding a bike along different sides of a triangular region. In the second activity they find internal diagonals of rectangular prisms.

### Learning Goals

Teacher Facing

• Describe (orally) situations that use right triangles, and explain how the Pythagorean Theorem could help solve problems in those situations.
• Use the Pythagorean Theorem to solve problems within a context, and explain (orally) how to organize the reasoning.

### Student Facing

Let’s explore some applications of the Pythagorean Theorem.

### Student Facing

• I can use the Pythagorean Theorem to solve problems.

### Glossary Entries

• Pythagorean Theorem

The Pythagorean Theorem describes the relationship between the side lengths of right triangles.

The diagram shows a right triangle with squares built on each side.  If we add the areas of the two small squares, we get the area of the larger square.

The square of the hypotenuse is equal to the sum of the squares of the legs. This is written as $$a^2+b^2=c^2$$.

• hypotenuse

The hypotenuse is the side of a right triangle that is opposite the right angle. It is the longest side of a right triangle.

Here are some right triangles. Each hypotenuse is labeled.

• legs

The legs of a right triangle are the sides that make the right angle.

Here are some right triangles. Each leg is labeled.