Pythagorean theorem worksheet

The Pythagorean theorem worksheet below has been carefully put together in order to help anyone see and understand why the Pythagorean theorem works. Teachers can use it as part of a lesson plan so that they can introduce students to the Pythagorean theorem. Scroll down to print the worksheet.

Name: ____________________

Date: _____________________

1. Use the figure above about the Pythagorean theorem to answer the following questions.

a. What is the area of square A ? __________

b. What is the area of square B ? __________

2.

a. What is the area of the triangle ? __________

b. How many of the triangle can fit in square C ? ___________

c. What is the area of the square C ? _________

3 . What is the relationship among the areas of the squares? (Hint: write an equation) _________

4. Using the equation you found in 3., write a formula for the Pythagorean theorem. __________

5. Find the missing length of the figure below

6. Find the missing length of the figure below

7. Find the missing length of the figure below

8. Find the missing length of the figure below if 2 squares represent 1 unit. 

Here is what the Pythagorean theorem worksheet will help students do.

1. Looking at the areas of the squares on each of the sides of the triangles shown on the graph paper.

2. Analyze the areas found for the three squares in order to write the relationship between the area of square C and the areas of square A and square B.

3. Use the relationship between the areas of the squares to write down the Pythagorean theorem.

Moreover, students will use the Pythagorean theorem worksheet to do find the length of c or the hypotenuse when a and b are known.

An example showing how to use the Pythagorean theorem

Use the Pythagorean theorem and the figure below to find the length of the hypotenuse or c.

c² = a² + b²

1. Find a and b by counting the units. We see that a = 10 and b = 8

2. Substitute 10 and 8 in the formula

c² = 10² + 8²

Find the sum of the squares 

c² = 100 + 64

c² = 164

Take the square root of the sum.

c = square root of 164 = 12.80

The length of the hypotenuse is 12.80.