These worksheets will give your students practice in using the Pythagorean Theorem to solve problems.

What is the Pythagorean Theorem? Pythagorean theorem describes the relation between the sides of a right-angled triangle. The Pythagorean formula is applied on a right-angled triangle and is used to determine the hypotenuse, base and the perpendicular of the triangle. The theorem states that: "In a right-angled triangle, the square of the hypotenuse side is equal to the squares of the perpendicular side and the base side." The hypotenuse is the longest side, and perpendicular is the side opposite to the hypotenuse side. Consider the triangle above, where a is the perpendicular side, b is the base side, and c is the hypotenuse. According to the definition of the Pythagorean theorem, the formula would be written as: c2 = a2 + b2

When a triangle has a right-angle, we can use the sum of the squares of each leg of the triangle to find the squared value of the hypotenuse. It can be rearranged to find the length of any of the sides. The Pythagorean Theorem has so many different applications to everyday life that it is not even funny. The theorem allows us to completely understand a right-triangle system with ease. It is used measure distances that are applicable to everything from measuring a deck about to be constructed or building a skyscraper. Your students will use the theorem to solve for variables for given triangles. Some questions may be in the form of word problems. Students should be familiar with different types of triangles.

Print Pythagorean Theorem Worksheets

Introduction Lesson

This worksheet explains how to use the Pythagorean theorem. A sample problem is solved, and two practice problems are provided.

Introduction Worksheet

Students will use the theorem to solve these triangle based problems.

Practice Sheet

Example problem: Let the distance of the ship from its starting point be x km. We can draw a diagram of the ship's voyage on a set of axes, with the horizontal axis representing east and the vertical axis representing north. The ship is at the point P and it started at the origin. There is a right angle at A.

Review and Practice

Example problem: The foot of an Iron ladder is placed 30 feet from a wall. If the top of the ladder rests 50 feet up on the wall, how long is the ladder?

Quiz Part I

Students will demonstrate their proficiency in using the Pythagorean theorem to solve problems.

Quiz Part 2

These are the more visual based problems.

Introduction Check

Students will use the theorem to solve problems. Space is included for students to copy the correct answer when given.

Using the Theorem Lesson

The Pythagorean Theorem is a formula relating the lengths of the three sides of a right triangle. It is used when we know the length of two sides of a right triangle and we need to get the length of the third side.

Applying Lesson and Practice

This worksheet explains how to find the missing side length of a given triangle. A sample problem word problem is solved, and two practice problems are provided.

Active Worksheet

Students will use the theorem to solve problems involving right triangles.

Application Practice

For each right triangle provided, students will solve for the missing side length.

Set of Drills

Students will write the equation according to the Pythagorean theorem for each triangle and indicate whether or not the side measurements provided are correct. Eight problems are provided.

Application Warm Up

Students will find the diagonals of the squares. Three problems are provided.

Solve for the Missing Side Lesson

This worksheet explains how to solve for the missing side measurement of a triangle. A sample problem is solved, and two practice problems are provided.

Solve for the Missing Side Worksheet

Students will solve for the missing side measurement of a triangle.

Solve for the Missing Side Practice

Students will solve for x.

More Review Worksheet

The Pythagorean theorem is reviewed and we use it for our own benefit. A sample problem is solved.

Skill Practice

Students will solve for the missing side measurement of a triangle.

Missing Side Quiz

Students will use the theorem to find the missing side measure.

Solve for the Missing Side Check

Students will solve for the missing side measurement of a triangle. Three problems are provided, and space is included for students to copy the correct answer when given.

Word Problem Lesson

This worksheet explains how to solve for the hypotenuse of a triangle. A sample problem is solved, and two practice problems are provided.

Word Problem Worksheet

If the sides of an isosceles right triangle are 4 inches long, approximate the length of the hypotenuse to the nearest whole number.

More Word Problem Practice

If the legs of an isosceles right triangle are 5 inches long, approximate the length of the hypotenuse to the nearest whole number.

Word Problem Review

We review with this problem: One leg of a triangular plate is 4 cm and other leg is of 3 cm. What is the hypotenuse?

Word Problem Review Sheet 2

Students will solve the word problems by using the Pythagorean Theorem.

Word Problem Quiz

Students will demonstrate their proficiency using the Pythagorean Theorem to solve word problems.

Quick Check

Example problem: Matt is flying a glider. He goes 5 km south and then 7 km west. How far is he from his starting point?

Solve for the Third Side Lesson

This worksheet explains how to use the Pythagorean theorem to determine the length of the third side of a triangle. A sample problem is solved.

Lesson and Practice

Given the measure of two sides of a triangle, this worksheet explains how to use the Pythagorean theorem to determine the length of the third side. A sample problem word problem is solved, and two practice problems are provided.

Third Side Worksheet

Students will use the theorem to solve for the length of the third side of each triangle.

Solving Sides Sides Practice

For each right triangle provided, students will solve for the length of the third side.

The Pythagorean Theorem Show the Skill

Determine the length of the third side of the right triangle.

Side Warm Up

Students will solve for the third side of each triangle. Three problems are provided.

Assorted Practice Problems

Students will solve an assortment of problems using the Pythagorean theorem.

Mixed Practice Worksheet

Students will use the theorem to solve assorted problems.

Practice Drill Set

Sample drill: In a right triangle, find the length of the side not given. Give an exact answer and approximation to three decimal places. b = 6, c = 10

Practice Skills Check

Students will demonstrate familiarity with the Pythagorean theorem.

Refresher Practice

Students will demonstrate proficiency with the Pythagorean theorem to solve for the length of the third side of each triangle.

Third Side Lesson

We walk you through how to solve this problem: A wired gate is 3 m wide and 1.6 m tall. It needs braces welded to it as shown in the picture. Find the length of the braces.

Lesson and Practice

This worksheet explains how to use the Pythagorean theorem to find the area of an equilateral triangle. A sample problem word problem is solved, and two practice problems are provided.

Third Side Worksheet

Students will use the theorem to solve word problems.

Practice Worksheet

Here is an example: Gary takes a shortcut along the diagonal of a rectangular plot that is 25 cm wide and 17 cm long, instead of going along the sides. How much does that shorten his path?

My Drill

A 13 feet ladder is placed on the wall of a house so that its lower end is 5 feet from the wall. At what height does the ladder touch the house?

Practical Worksheet

Find the perimeter of given lots.