Pythagorean Theorem Worksheets

There are five sets of triangle worksheets:

• Triangle Sum Theorem
  
• Exterior Angle Theorem
  
• Area of Triangle
  
• Area of Triangle using Sine
  
• Pythagorean Theorem
  

Examples, solutions, videos, and worksheets to help grade 7 students learn how to use the Pythagorean Theorem.

How to use the Pythagorean Theorem?

There are five sets of Pythagorean Theorem worksheets:

• Find the length of the hypotenuse
• Find the length of a side
• Find the length in two steps
• Check for right triangle
• Pythagorean Theorem Word Problems

The Pythagorean Theorem also called the Pythagoras’ Theorem is a fundamental principle in geometry that relates the sides of a right triangle.

It states that in a right triangle (a triangle with one 90-degree angle), the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Mathematically, the Pythagorean Theorem can be expressed as:
c² = a² + b²

Where:

• c represents the length of the hypotenuse.
• a and b represent the lengths of the other two sides.

The Pythagorean Theorem is widely used to calculate the length of any one side of a right triangle when the lengths of the other two sides are known. It is an essential tool in geometry and has applications in various fields, including trigonometry, engineering, physics, and architecture.

The Pythagorean Theorem can be used in various ways, including:

• Finding length of any one side of a right triangle when the lengths of the other two sides are known.
• Checking if a Triangle is Right: You can use the theorem to check if a triangle is a right triangle by verifying if the relationship a² + b² = c² holds.
• Solving Problems Involving Right Triangles: The theorem is used to solve problems involving right triangles, such as finding distances, heights, or angles in various real-world situations.

For example, if you have a right triangle with one side (a) measuring 3 units and the other side (b) measuring 4 units, you can use the Pythagorean Theorem to find the length of the hypotenuse (c):

c² = a² + b²
c² = 3² + 4²
c² = 9 + 16
c² = 25

To find c, take the square root of both sides:

c = √25
c = 5

So, the length of the hypotenuse (c) is 5 units. This illustrates how the Pythagorean Theorem can be used to solve for side lengths in a right triangle.

Have a look at this video if you need to review how to use the Pythagorean Theorem.

• The Pythagorean Theorem

Click on the following worksheet to get a printable pdf document.
Scroll down the page for more Pythagorean Theorem Worksheets.

 

More Pythagorean Theorem Worksheets

Printable
(Answers on the second page.)
Pythagorean Theorem Worksheet #1 (find hypotenuse)
Pythagorean Theorem Worksheet #2 (find a side)
Pythagorean Theorem Worksheet #3 (2-step)
Pythagorean Theorem Worksheet #4 (check for right triangle)
Pythagorean Theorem Worksheet #5 (word problems)

Online
Pythagorean Theorem
Find the missing side
Test for right triangle
Pythagorean Theorem Word Problems
Converse Pythagorean Theorem, Types of Triangles

Related Lessons & Worksheets

Area of Triangle using Sine

More Printable Worksheets

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