Bellwork: 2/12/18 (Block 3) Use the look for a pattern strategy to solve Exercises 1–3. 1. In a stadium, there are 10 seats in the 1st row, 13 seats in the 2nd row, 16 seats in the 3rd row, and so on. How many seats are in the 10th row? 2. Find the next three numbers in the sequence 20, 24, 21, 25, 22, 26, ... . 3. Sarah rents videos from a video rental store that charges a monthly rate of $9.95 plus $0.75 per video rental. If Sarah’s total monthly bill was $30.95, how many videos did she rent? 4. The Ito family is driving to Oklahoma from Texas. If they average 65 miles per hour, how far will they drive in hours? Course 3, Lesson 5-5

Course 3, Lesson 5-5 Common Core State Standards © Copyright 2010 Course 3, Lesson 5-5 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

ANSWERS 1. 37 seats 2. 23, 27, 24 3. 28 4. 227.5 miles Course 3, Lesson 5-5

HOW can algebraic concepts be applied to geometry? Course 3, Lesson 5-5

Geometry 8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational. Course 3, Lesson 5-5 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

Mathematical Practices Geometry Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. 4 Model with mathematics. 5 Use appropriate tools strategically. Course 3, Lesson 5-5 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

Objective The student will be able to: Use the Pythagorean Theorem to find missing sides of a right triangle Designed by Skip Tyler, Varina High School

What is a right triangle? REVIEW It is a triangle which has an angle that is ___ degrees. The two sides that make up the right angle are called ____. The side opposite the right angle is the ______________.

Course 3, Lesson 5-5 Common Core State Standards © Copyright 2010 Course 3, Lesson 5-5 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

Course 3, Lesson 5-5 Common Core State Standards © Copyright 2010 Course 3, Lesson 5-5 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

the missing length. Round to the nearest tenth if necessary. Step-by-Step Example 2. Write an equation you could use to find the length of the missing side of the right triangle. Then find the missing length. Round to the nearest tenth if necessary. 1 a2 + b2 = c2 Pythagorean Theorem 82 + b2 = 242 2 Replace a with 8 and c with 24. 3 64 + b2 = 576 Evaluate 82 and 242. 64 – 64 + b2 = 576 – 64 Subtract 64 from each side. 4 b2 = 512 Simplify. b = ±√512 Definition of square root 5 b ≈ 22.6 or –22.6 Use a calculator. The length of side b is about 22.6 meters. 6 Check for Reasonableness The hypotenuse is always the longest side in a right triangle. Since 22.6 is less than 24, the answer is reasonable. 7 Need Another Example?

Find the length of the leg, to the nearest hundredth, if c = 10 and b = 7. Solve for a. a2 = 100 - 49 a2 = 51 a = 7.14

Find the length of the missing side given a a= 4 and c = 5 1 3 6.4 9

could use to find the length of the missing side of the right Need Another Example? Write an equation you could use to find the length of the missing side of the right triangle shown. Then find the missing length. Round to the nearest tenth if necessary. a2 + 282 = 332; 17.5 in. Answer

Write an equation you could use to find the length of the hypotenuse of the right triangle shown. Then find the length. Round to the nearest tenth if necessary.

Course 3, Lesson 5-5 Common Core State Standards © Copyright 2010 Course 3, Lesson 5-5 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

Guided Practice pg. 426 (1-6)

How did what you learned today help you answer the Geometry How did what you learned today help you answer the HOW can algebraic concepts be applied to geometry? Course 3, Lesson 5-5

Independent Practice 1. ) pg. 415 (1-9) pg. 427 (1-6) 2 Independent Practice 1.) pg. 415 (1-9) pg. 427 (1-6) 2.) IXL Levels 8th grade (R.1) (R.2) (R.5)

Geometry Functions Ratios and Proportional Relationships Determine whether a triangle with side lengths of 1 centimeter, 2 centimeters, and 3 centimeters is a right triangle. Justify your response. Course 3, Lesson 5-5