Friday, We will use the Pythagorean Theorem to find an unknown length of a side.
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- Gwen Howard
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1 Learning Objective Name We will use the Pythagorean Theorem to find an unknown length of a side. CFU Friday,.8. What are we going to do? Activate Prior Knowledge 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. Use the chart to evaluate the following. x x Right Triangle Make Connection 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.
2 Concept Development The Pythagorean Theorem 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. Pythagorean Theorem If then the triangle is a right triangle, the square of the first leg plus the square of the second leg is equal to the square of the hypotenuse. The Pythagorean Theorem CANNOT be used: NOT a right triangle 6 cm 8 cm CFU 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)? 7? 9 9 A B C 9?? In your own words, describe the Pythagorean theorem. The Pythagorean Theorem describes. Vocabulary statement which can be proven mathematically
3 Skill Development/Guided Practice The Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. Use the Pythagorean Theorem to find an unknown length of a side. 4 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. a Substitute 4 the two known values and solve. Interpret 5 the solution.. Find the length of YZ. ( YZ means the line segment starting at point Y and ending at point Z.) Z cm Y 9 cm X is. YZ. Find the length of XZ. Z 5 in X in Y is. XZ CFU 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? Vocabulary figure out find (synonym) 4 replace (synonym) 5 explain
4 Skill Development/Guided Practice (continued) The Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. Use the Pythagorean Theorem to find an unknown length of a side. 4 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. a Substitute the two known values and solve. Interpret the solution.. Find the length of side p. 6 in 0 in p p is. 4. Find the length of side w. 4 cm 5 cm w w is. CFU 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?
5 Skill Development/Guided Practice (continued) The Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. Use the Pythagorean Theorem to find an unknown length of a side. 4 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. a Substitute the two known values and solve. Interpret the solution. 5. In the figure below, D is the midpoint of AC, and BD is perpendicular to AC. What is the length of BD? B 6 in BD is. A D C 0 in 6. In the figure below, H is the midpoint of EG, and FH is perpendicular to EG. What is the length of FH? F 0 in is. FH E H 4 in G CFU 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?
6 Skill Development/Guided Practice (continued) The Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. Use the Pythagorean Theorem to find an unknown length of a side. 4 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. a Substitute the two known values and solve. Interpret the solution. 7. In the figure below, M is the midpoint of JL, and is perpendicular to JL. KM is 5 cm. JL is 6 cm. What is the length of JK? KM J M K JK is. 8. In the figure below, Q is the midpoint of OP, and is perpendicular to OP. NQ is 4 cm. OP is 4 cm. What is the length of ON? NQ O L Q N CFU ON is. P 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?
7 Relevance The Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. Using the Pythagorean Theorem will help you find the distance between locations. Using the Pythagorean Theorem will help you do well on tests. Sample Test Question: Sample Test Question: CFU 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?
8 The Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. Skill Closure Use the Pythagorean Theorem to find an unknown length of a side. 4 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. a Substitute the two known values and solve. Interpret the solution.. Find the length of side d. d 6 cm 8 cm Access Common Core With which triangle below could you use the Pythagorean Theorem to find the unknown length? Explain why you cannot use the Pythagorean Theorem on the other.? A 0 Summary Closure d is.? B What did you learn today about using the Pythagorean Theorem? (Pair-Share) Use words from the word bank. Day Day 6 6
9 Independent Practice Name The Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. Use the Pythagorean Theorem to find an unknown length of a side. 4 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. a Substitute the two known values and solve. Interpret the solution.. Find the length of ST. S 8 ft R 5 ft T ST is.. Find the length of side g. 5 in 0 in g g is.
10 Independent Practice (continued) The Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. Use the Pythagorean Theorem to find an unknown length of a side. 4 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. a Substitute the two known values and solve. Interpret the solution.. In the figure below, W is the midpoint of XZ, and YW is perpendicular to XZ. What is the length of YW? Y 5 in X W Z is. YW 4 in 4. In the figure below, B is the midpoint of AC, and is perpendicular to AC. BD is 4 cm. AC is 6 cm. What is the length of AD? BD A B D AD is. C
11 Periodic Review Name. Find the length of side c. 0 m c 4 m c is.. Find the length of side y. y 5 in 4 in y is.. In the figure below, O is the midpoint of PQ, and NO is perpendicular to PQ. NO is 0 cm. PQ is 0 cm. What is the length of NP? P N O NP is. Q
12 Access Common Core Name For questions a d, choose Yes or No to indicate whether the statement is true or false. 5 m p m a. The Pythagorean Theorem can be used to solve for the unknown side length because the triangle is a right triangle. Yes No b. The unknown side length (p) can be solved for using the equation 5 + p = Yes No c. The length of the unknown side (p) will be shorter than the other two sides. Yes No d. The length of side p is m. Yes No
13 Periodic Review Name. In the figure below, Y is the midpoint of XZ, and YWis perpendicular to XZ. YW is 6 cm. XZ is 60 cm. What is the length of XW? X Y Z W is.. Find the length of MN. M 0 in O in MN is. N Access Common Core Greg used the Pythagorean Theorem in the triangle above. He found that the unknown side length (q) was 6 in. Explain why Greg is incorrect using pictures, math, or words.
14 Periodic Review Name. Find the length of side a. 6 cm 9 cm a a is.. Find the length of side c. 4 m 8 m c c is.. In the figure below, E is the midpoint of DF, and GE is perpendicular to DF. What is the length of GE? G 5 in D E 8 in F GE is.
15 Access Common Core Lilia s House 5 miles b 9 miles Kurt s House Kurt is driving to Lilia s house. On a straight line, his house is 5 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.
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