1. What are we going to do? CFU On your whiteboards, draw a right triangle. Label the hypotenuse. Label the legs. Students, you already know the parts of a right triangle. You also know how to square and square root numbers. Now, we will find unknown lengths of the hypotenuse and legs of right triangles using the Pythagorean Theorem. Make Connection Learning Objective Activate Prior Knowledge We will use the Pythagorean Theorem to find an unknown length of a side. A right triangle is a triangle with a 90  angle. The hypotenuse is the side opposite the right angle. The legs are the two shorter sides of the right triangle. Right Triangle 2. 4. 40020 36119 32418 28917 25616 22515 19614 16913 Use the chart to evaluate the following. 1. 3. Wednesday, 11/13/13 CA Standard: 7.MG3.3 Common Core State Standards 8.G.7

2. 6 cm 8 cm The Pythagorean Theorem 1 describes the relationship between the lengths of the sides of a right triangle. The Pythagorean Theorem can be used to solve for an unknown side length in a right triangle. For which triangle(s) could you use the Pythagorean Theorem to find the unknown side length? How do you know? Why can you not use the Pythagorean Theorem on the other triangle(s)? In your own words, describe the Pythagorean theorem. “The Pythagorean Theorem describes _____.” CFU Concept Development 1 statement which can be proven mathematically Vocabulary Pythagorean Theorem If the triangle is a right triangle, then the square of the first leg plus the square of the second leg is equal to the square of the hypotenuse. 10 cm 6 cm 8 cm ? ft 5 ft 12 ft NOT a right triangle The Pythagorean Theorem CANNOT be used: 9 11 ? 712 ? 9 9 ?

3. Concept Development (Clarification and CFU) The Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. If the triangle is a right triangle, then the square of the first leg plus the square of the second leg is equal to the square of the hypotenuse. Using the diagram below, describe the relationship between the square of the legs and the square of the hypotenuse of the right triangle. CFU 4 5 3 = hyp 2 leg 2 +

4. Determine 2 if the Pythagorean Theorem can be used. Identify 3 the hypotenuse and two legs of the right triangle. (record) Find the unknown length of the side using the Pythagorean Theorem. Substitute 4 the two known values and solve. Interpret 5 the solution. Use the Pythagorean Theorem to find an unknown length of a side. 1 2 3 4 a Skill Development/Guided Practice How did I/you determine if the Pythagorean Theorem can be used? How did I/you identify the hypotenuse and two legs of the right triangle? How did I/you find the unknown side length using the Pythagorean Theorem? CFU 1 2 3 Pythagorean Theorem leg 2 + leg 2 = hyp 2 The Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. 1. Find the length of. ( means the line segment starting at point Y and ending at point Z.) 2. Find the length of. 5 in 12 in 9 cm 12 cm leg = hyp = The length of the ___________ is _______. leg = hyp = The length of the ___________ is _______. 2 figure out 3 find (synonym) 4 replace (synonym) 5 explain Vocabulary

5. Skill Development/Guided Practice (continued) Determine if the Pythagorean Theorem can be used. Identify the hypotenuse and two legs of the right triangle. (record) Find the unknown length of the side using the Pythagorean Theorem. Substitute the two known values and solve. Interpret the solution. Use the Pythagorean Theorem to find an unknown length of a side. 1 2 3 4 a How did I/you determine if the Pythagorean Theorem can be used? How did I/you identify the hypotenuse and two legs of the right triangle? How did I/you find the unknown side length using the Pythagorean Theorem? CFU 2 2 3 Pythagorean Theorem leg 2 + leg 2 = hyp 2 The Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. 3. Find the length of side p.4. Find the length of side w. 6 in 10 in p 4 cm 5 cm w leg = hyp = The length of the ___________ p is _______. leg = hyp = The length of the ___________ w is _______.

6. Determine if the Pythagorean Theorem can be used. Identify the hypotenuse and two legs of the right triangle. (record) Find the unknown length of the side using the Pythagorean Theorem. Substitute the two known values and solve. Interpret the solution. Use the Pythagorean Theorem to find an unknown length of a side. 1 2 3 4 a How did I/you determine if the Pythagorean Theorem can be used? How did I/you identify the hypotenuse and two legs of the right triangle? How did I/you find the unknown side length using the Pythagorean Theorem? CFU 1 2 3 Pythagorean Theorem leg 2 + leg 2 = hyp 2 The Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. 5. In the figure below, D is the midpoint of, and is perpendicular to. What is the length of ? 6. In the figure below, H is the midpoint of, and is perpendicular to. What is the length of ? A D C B 20 in 26 in H E F G 24 in 20 in leg = hyp = The length of the ___________ is _______. leg = hyp = The length of the ___________ is _______. Skill Development/Guided Practice (continued)

7. Determine if the Pythagorean Theorem can be used. Identify the hypotenuse and two legs of the right triangle. (record) Find the unknown length of the side using the Pythagorean Theorem. Substitute the two known values and solve. Interpret the solution. Use the Pythagorean Theorem to find an unknown length of a side. 1 2 3 4 a How did I/you determine if the Pythagorean Theorem can be used? How did I/you identify the hypotenuse and two legs of the right triangle? How did I/you find the unknown side length using the Pythagorean Theorem? CFU 1 2 3 Pythagorean Theorem leg 2 + leg 2 = hyp 2 The Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. 7. In the figure below, M is the midpoint of, and is perpendicular to. is 15 cm. is 16 cm. What is the length of ? 8. In the figure below, Q is the midpoint of, and is perpendicular to. is 24 cm. is 14 cm. What is the length of ? L M J K O Q P N leg = hyp = The length of the ___________ is _______. leg = hyp = The length of the ___________ is _______. Skill Development/Guided Practice (continued)

8. Using the Pythagorean Theorem will help you find the distance between locations. Using the Pythagorean Theorem will help you do well on tests. 1 Does anyone else have another reason why it is relevant to use the Pythagorean Theorem? (Pair–Share) Why is it relevant to use the Pythagorean Theorem? You may give me one of my reasons or one of your own. Which reason is more relevant to you? Why? CFU 2 Relevance The Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. How long is the Salinas River from King City to Soledad? Salinas River King City Soledad 16mi 12mi Sample Test Question:

9. Summary Closure Access Common Core The Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. Determine if the Pythagorean Theorem can be used. Identify the hypotenuse and two legs of the right triangle. (record) Find the unknown length of the side using the Pythagorean Theorem. Substitute the two known values and solve. Interpret the solution. Use the Pythagorean Theorem to find an unknown length of a side. 1 2 3 4 a With which triangle on the left could you use the Pythagorean Theorem to find the unknown length? Explain why you cannot use the Pythagorean Theorem on the other. 10 12 ? A 6 6 ? B Pythagorean Theorem leg 2 + leg 2 = hyp 2 Skill Closure 1. Find the length of side d. 8 cm 6 cm d leg = hyp = The length of the ___________ d is _______. What did you learn today about using the Pythagorean Theorem? (Pair-Share) Use words from the word bank. Word Bank Pythagorean Theorem right triangle side hypotenuse leg length

10. Independent Practice Determine if the Pythagorean Theorem can be used. Identify the hypotenuse and two legs of the right triangle. (record) Find the unknown length of the side using the Pythagorean Theorem. Substitute the two known values and solve. Interpret the solution. Use the Pythagorean Theorem to find an unknown length of a side. 1 2 3 4 a Pythagorean Theorem leg 2 + leg 2 = hyp 2 The Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. 1. Find the length of. S T R 15 ft 8 ft 2. Find the length of side g. 20 in 25 in g leg = hyp = The length of the ___________ is _______. leg = hyp = The length of the ___________ g is _______.

11. Determine if the Pythagorean Theorem can be used. Identify the hypotenuse and two legs of the right triangle. (record) Find the unknown length of the side using the Pythagorean Theorem. Substitute the two known values and solve. Interpret the solution. Use the Pythagorean Theorem to find an unknown length of a side. 1 2 3 4 a Pythagorean Theorem leg 2 + leg 2 = hyp 2 The Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. Independent Practice (continued) 3. In the figure below, W is the midpoint of, and is perpendicular to. What is the length of ? 4. In the figure below, B is the midpoint of, and is perpendicular to. is 4 cm. is 6 cm. What is the length of ? 24 in 15 in leg = hyp = The length of the ___________ is _______. leg = hyp = The length of the ___________ is _______.

12. Periodic Review 1 1. Find the length of side c.2. Find the length of side y. 24 m 10 m c 24 in 25 in y leg = hyp = The length of the ___________ c is _______. leg = hyp = The length of the ___________ y is _______. 3. In the figure below, O is the midpoint of, and is perpendicular to. is 20 cm. is 30 cm. What is the length of ? leg = hyp = The length of the ___________ is _______.

13. Access Common Core For questions 1a–1d, choose Yes or No to indicate whether the statement is true or false. 12 m 5 m p 1a. YesNo The Pythagorean Theorem can be used to solve for the unknown side length because the triangle is a right triangle. 1b. YesNo The unknown side length (p) can be solved for using the equation 5 2 + p 2 = 12 2 1c. YesNo The length of the unknown side (p) will be shorter than the other two sides. 1d. YesNo The length of side p is 13 m.

14. Access Common Core 80° 55°45° 8 in 10 in q Greg used the Pythagorean Theorem in the triangle. He found that the unknown side length (q) was 6 in. Explain why Greg is incorrect using pictures, math, or words. Periodic Review 2 1. In the figure below, Y is the midpoint of, and is perpendicular to. is 16 cm. is 60 cm. What is the length of ? 2. Find the length of. N M O 20 in 21 in leg = hyp = The length of the ___________ is _______. leg = hyp = The length of the ___________ is _______.

15. 2. Find the length of side c. 3. In the figure below, E is the midpoint of, and is perpendicular to. What is the length of ? E D G F 18 in 15 in 24 m 18 m c leg = hyp = The length of the ___________ c is _______. leg = hyp = The length of the ___________ is _______. 1. Find the length of side a. 36 cm 39 cm a leg = hyp = The length of the ___________ a is _______. Periodic Review 3

16. Access Common Core Lilia’s House Kurt’s House 9 miles b 15 miles Kurt is driving to Lilia’s house. On a straight line, his house is 15 miles from Lilia’s, however, he must drive to her house using roads. He heads west for 9 miles then turns right heading north. How far north does Kurt have to travel before reaching Lilia’s house? Explain your answer below using pictures, math, or words.