Pythagorean Theorem Objective The purpose of this Web Quest is to learn about arguably the most important theorem in Geometry, the Pythagorean Theorem. We will also explore applications and uses for this fundamental theorem in everyday life.

Tasks: Research Pythagoras and the Pythagorean Theorem through websites and videos. Complete worksheets using the Pythagorean Theorem Create a real-world word problem that uses the Pythagorean Theorem. Write a summary discussing your new understanding of Pythagoras and/ or the Pythagorean Theorem. DUE Friday, January 16th.

Research You will first research the history of Pythagoras and the Pythagorean Theorem. Begin by reviewing the videos and websites below: History of Pythagoras Brief History of the Pythagorean Theorem Information about Pythagoras Donald and Pythagoras More on the Pythagorean Theorem

PowerPoint Lesson Attachments can be accessed by clicking on the document. If you are having any issues please go to the Attachments folder on the Class Fusion Page and view the PowerPoint Lesson about the Pythagorean Theorem and any worksheets.

More Lessons On The Pythagorean Theorem. Please view the following lessons about The Pythagorean Theorem. More examples at the end of this power point, just click on the pencil to bring you to the examples. Introduction to the Pythagorean Theorem Real World Example

Applying the Pythagorean Theorem Then use the information from your research to answer the questions on the Pythagorean Theorem Web Quest worksheets. Do Worksheet 1 and Worksheet 2. Record all answers on the answer sheet. Remember to turn in all work with your answers. DUE Friday, January 16th.

Create: Create a real world example word problem that implements the Pythagorean Theorem. use a personal interest or hobby as your guide. DUE Friday, January 16th.

Putting it All Together I hope that you enjoyed your Web Quest and learning about Pythagoras and the Pythagorean Theorem. To conclude this project, please write a brief summary about your experiences while exploring the Pythagorean Theorem. Identify two new ideas or facts that you learned during this quest. Your summary should be a minimum of two age/ grade appropriate, full, grammatically correct paragraphs. DUE Friday, January 16th.

Rubric Pythagorean Theorem Rubric Please review the attached rubric so you are completely aware how this TEST grade is being assessed. Any questions at all, please come see me. DUE Friday, January 16th.

More Examples The following slides have examples in solving problems with the Pythagorean Theorem, including Pythagorean Triples.

The Pythagorean Theorem is probably the most famous mathematical relationship. It states that in a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. a2 + b2 = c2

The side “c” is always the hypotenuse The side “c” is always the hypotenuse. It is the side directly across from the right angle.

Example 1: Using the Pythagorean Theorem Find the value of x. Give your answer in simplest radical form. The “x” is the “c” side because it is the hypotenuse. You know you are solving for “c”.

Example 1: Using the Pythagorean Theorem Find the value of x. Give your answer in simplest radical form. a2 + b2 = c2 Pythagorean Theorem 22 + 62 = x2 Substitute 2 for a, 6 for b, and x for c.

Example 1: Using the Pythagorean Theorem Find the value of x. Give your answer in simplest radical form. a2 + b2 = c2 Pythagorean Theorem 22 + 62 = x2 Substitute 2 for a, 6 for b, and x for c. 4 + 36 = x2 Calculate 40 = x2 Simplify

Example 1: Using the Pythagorean Theorem Find the value of x. Give your answer in simplest radical form. a2 + b2 = c2 Pythagorean Theorem 22 + 62 = x2 Substitute 2 for a, 6 for b, and x for c. 40 = x2 Simplify. Find the positive square root.

Find the value of x. Give your answer in simplest radical form. Check It Out! Example 2 Find the value of x. Give your answer in simplest radical form. a2 + b2 = c2 Pythagorean Theorem 42 + 82 = x2 Substitute 4 for a, 8 for b, and x for c. 80 = x2 Simplify. Find the positive square root. Simplify the radical.

Now let’s look at some Challenge Problems where we incorporate our algebra into the Pythagorean Theorem!

Example 3: Using the Pythagorean Theorem Find the value of x. Give your answer in simplest radical form. a2 + b2 = c2 Pythagorean Theorem (x – 2)2 + 42 = x2 Substitute x – 2 for a, 4 for b, and x for c. x2 – 4x + 4 + 16 = x2 Multiply. –4x + 20 = 0 Combine like terms. 20 = 4x Add 4x to both sides. 5 = x Divide both sides by 4.

Find the value of x. Give your answer in simplest radical form. Check It Out! Example 4 Find the value of x. Give your answer in simplest radical form. a2 + b2 = c2 Pythagorean Theorem Substitute x for a, 12 for b, and x + 4 for c. x2 + 122 = (x + 4)2 x2 + 144 = x2 + 8x + 16 Multiply. 128 = 8x Combine like terms. Divide both sides by 8. 16 = x

Example 5: Crafts Application Randy is building a rectangular picture frame. He wants the ratio of the length to the width to be 3:1 and the diagonal to be 12 centimeters. How wide should the frame be? Round to the nearest tenth of a centimeter.

Example 5: Crafts Application Randy is building a rectangular picture frame. He wants the ratio of the length to the width to be 3:1 and the diagonal to be 12 centimeters. How wide should the frame be? Round to the nearest tenth of a centimeter. Let l and w be the length and width in centimeters of the picture. Then l:w = 3:1, so l = 3w.

Example 5 Continued Pythagorean Theorem a2 + b2 = c2 Substitute 3w for a, w for b, and 12 for c. (3w)2 + w2 = 122 10w2 = 144 Multiply and combine like terms. Divide both sides by 10. Find the positive square root and round.

Check It Out! Example 6 What if...? According to the recommended safety ratio of 4:1, how high will a 30-foot ladder reach when placed against a wall? Round to the nearest inch.

Check It Out! Example 6 What if...? According to the recommended safety ratio of 4:1, how high will a 30-foot ladder reach when placed against a wall? Round to the nearest inch. Let x be the distance in feet from the foot of the ladder to the base of the wall. Then 4x is the distance in feet from the top of the ladder to the base of the wall.

Check It Out! Example 6 Continued a2 + b2 = c2 Pythagorean Theorem (4x)2 + x2 = 302 Substitute 4x for a, x for b, and 30 for c. 17x2 = 900 Multiply and combine like terms. Since 4x is the distance in feet from the top of the ladder to the base of the wall, 4(7.28)  29 ft 1 in.

A set of three nonzero whole numbers a, b, and c such that a2 + b2 = c2 is called a Pythagorean triple.

Example 7: Identifying Pythagorean Triples Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain. a2 + b2 = c2 Pythagorean Theorem 142 + 482 = c2 Substitute 14 for a and 48 for b. 2500 = c2 Multiply and add. 50 = c Find the positive square root. The side lengths are nonzero whole numbers that satisfy the equation a2 + b2 = c2, so they form a Pythagorean triple.

Example 8: Identifying Pythagorean Triples Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain. a2 + b2 = c2 Pythagorean Theorem 42 + b2 = 122 Substitute 4 for a and 12 for c. b2 = 128 Multiply and subtract 16 from both sides. Find the positive square root. The side lengths do not form a Pythagorean triple because is not a whole number.

Credits Holt Online Learning presentations my.hrw.com