5 4 The Pythagorean Theorem Objectives Determine the

5. 4 The Pythagorean Theorem Objectives: - Determine the length of a missing side of a right triangle. Warm-Up: REDUCE

VOCABULARY �

a c b Pythagorean Theorem 2 a 2 +b Legs 2 =c Hypotenuse Right Triangles only! Note: when you apply the Pythagorean Theorem use the principal square root because distance and length cannot be negative.

Identify the missing lengths. Express your answer, in both decimal & reduced radical form. 12 8

VOCABULARY Pythagorean Triple Sets of positive integers a, b, & c such that a 2 + b 2 = c 2 EXAMPLES: 3, 4, 5 9, 40, 41 8, 15, 17 11, 60, 61

Find the third side so that the three numbers for a Pythagorean Triple. 5, 13 7, 24

The Pythagorean Theorem: For any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. Converse of the Pythagorean Theorem: If the square of the length of one side of a triangle equals the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Consider the converse of the Pythagorean Theorem Is the following triangle a right triangle? 3. 7 3. 5 1. 2

The bottom of a ladder is 6 feet from the base of a building and reaches a height of 12 feet on the side of the building. How long is the ladder? Express your answer, in both decimal & reduced radical form.

Television sets are measured by the length of their diagonal. Your friend is going to give you his old TV. He claims the screen is 20 inches and it has a length of 15 inches. How wide is the television set? Express your answer, in both decimal & reduced radical form. x 20 15

HSPA PROBLEM OF THE DAY: A boat leaves its dock and travels East for 6 miles and then South for 8 miles to reach its destination. Draw a vector diagram to model the path of the boat. If the boat traveled from the dock directly to its destination how many miles would it have gone? Show all of your work and explain how you arrived at your solution. N E W S

When we are solving problems that utilize the Pythagorean Theorem and the results are not integers there are two ways to write out solutions: as decimals and as radicals. Collins Writing Type 1: What is the benefit of writing our solution in radical form opposed to writing the solution as a decimal? RESULTS ARE EXACT 3 lines 2 minutes

Collins Writing: ________________________________ 3 lines 2 minutes

Mike is loading his truck in preparation for painting the exterior of a building. He has two ladders. The longer ladder needs to be further away from the base of the building for stability. The shorter ladder can be placed closer to the base of the building. He wants to reach as high as possible on his next project and is trying to decide which ladder to bring to the job. Which of the following scenarios will allow the painter to reach higher on the building? Draw and label a picture to model each scenario and show all of your work. Ladder 1 is 17 ft long and must be placed 15 ft from the base of the building. Ladder 2 is 13 ft long and can be placed 5 ft from the base of the building. EXIT TICKET

Homework: Practice Worksheet

5. 4 The Pythagorean Theorem Objectives: - Use the Pythagorean Inequalities to determine if a triangle is acute, right, or obtuse. Warm-Up: If you have SIX people in a room and each person shakes hands with every other person exactly once, how many total handshakes happen?

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VOCABULARY right triangle: a triangle that has one right angle. obtuse triangle: a triangle that has one obtuse angle. acute triangle: a triangle with three acute angles.

Examples: Determine if the triangle is right, acute, or obtuse based on the given lengths of its sides. 7, 8, 12 7, 24, 25 10, 15, 13 14, 7, 9

Examples: Find the area of the shaded region. Round your answer to the nearest tenth. 18 24

Examples: Find the area of the shaded region. Round your answer to the nearest tenth. 8 16

Find the area of the shaded region. Examples: Round your answer to the nearest tenth. 13 4 3

Find the perimeter. Examples: Round your answer to the nearest tenth. 30 8 10

Examples: Find the area. Round your answer to the nearest tenth. 12

Homework: Pages 326 -327; Numbers 14 -30