# Pythagorean Theorem Worksheets

When a triangle has a right side (measuring ninety degrees) and you extend each side with a square, the biggest square has the same exact are as the sum of the squares of the other two sides. If we labelled the longest side c and the other two sides (legs) a and b, we could sum up that phenomena with the equation a^{2} + b^{2} = c^{2}. We term the longest side, that opposite the right angle, the hypotenuse. As you gather by the algebra, if you know the measures of any two sides of a right triangle, you can use this theorem to determine the third side. Pythagorean Theorem lends itself to all form of building and construction because it allows you to easily determine the length of any material that we using as long as you have two materials that meet at a right angle. Sailors use this all the time to find the shortest route between two points. You will find many applications in the field of surveying when cartographers and engineers are constructing maps that indicate steepness and slopes of areas.

### Aligned Standard: Grade 8 Geometry - 8.G.B.8

- Applying the Pythagorean Theorem Step-by-Step Lesson- The side that is missing is defined as the hypotenuse. We can tell this because it is directly opposite the right angle.
- In Action Guided Lesson - Example: Given a right triangle with a hypotenuse of 27 and a leg of 17, what is the measure of the missing leg?
- Guided Lesson Explanation - If this is a right triangle it will work out when the Pythagorean Theorem is applied to it. This means it will flow in the formula: leg
^{2}+ leg^{2}= hypotenuse^{2} - Are They Right Triangles? - Determine the classification of these shapes.
- Skills Review - We explore every way this topic can be looked at.

- Answer Keys - These are for all the unlocked materials above.

### Review Sheets

The coordinate graph makes it much more understandable than just labeling sides.

- Review 1 - We will look this from the diagram perspective and in word form.
- Review 2 - Another go at this series of skills.

### Homework Sheets

The coordinate graph makes it much more understandable than just labeling sides.

- Homework 1 - We will see if these shapes will work for us.
- Homework 2 - Another approach at the first version.
- Homework 3 - All of these shapes are much more narrow.
- Homework 4 - You will find decimal lengths to work with.

### Practice Worksheets

We start to find random distances between points.

- Practice 1 - You will work with some really scaled down sides.
- Practice 2 - We orientate these shapes from all directions.
- Practice 3 - This is a basic look at this skill.
- Practice 4 - More decimal lengths to work with.

### Math Skill Quizzes

Here are more like problems to help you master this topic.

- Quiz 1 - Use the Pythagorean theorem to find the length of the missing side of the right triangle.
- Quiz 2 - Apply this formula to see if you can determine that missing side.
- Quiz 3 - Time break out the decimal form one more time.

### How is the Pythagorean Theorem Used Every in Life?

The history behind how this theorem was conceived is almost fiction-like. Pythagoras was a Greek mathematician, among other things. He was born around 500 B.C. He founded a group called the Brotherhood of Pythagoreans which was devoted towards the study of mathematics. The theorem is credited to Pythagoras, but historians do strongly suggest that it was the effort of this group.

More than 2,500 years later this math still holds up and we use this theorem in our daily lives without even realizing it. It goes without saying that most forms of architecture and construction projects heavily rely on this to form straight lines in their buildings. It also is the foundation of how the angle of roofing is pitched on almost all structures. All the beams and materials used are dependent on this calculation. Something as simple as determining how to optimal position ladders against a wall for safety are calculated in this manner as well.

The Brotherhood of Pythagoreans probably never thought that large water vessels would depend on their math to circumnavigate the Earth's oceans. From very short distances to long, understanding the best path is often a product of this theorem. It also helps ships Captains determine how to interest or disrupt enemies in battle. Watch just about any war movie that involves a ship or a submarine and you will see mathematical compasses and rulers putting this to work.