Prentice Hall Lesson 11.2 EQ: What is the Pythagorean Theorem? BOP:

Solution to BOP: Homework Questions?

mi mi ALGEBRA 1 LESSON 11-1 pages 581–583 Exercises – x x mi a

56.a = 180 = 36 5 = 6 5 b.Answers may vary. Sample: a = 36, b = 5; a = 9, b = not simplest form; radical in the denominator of a fraction 53.not simplest form; radical in the denominator of a fraction x ALGEBRA 1 LESSON

78. seconds 79.C 80.F 81.B 82.I 83.A = 96 ft 2 s = 96 = 16 6 = 4 6 ft 69. –3 ± a. 50 = 25 2 = 25 2 = 5 2 b.The radicand has no perfect-square factors other than Answers may vary. Sample: 12, 27, a. 2 6 in. b in x ALGEBRA 1 LESSON ab 5b 11-1

Prentice Hall Lesson 11.2 What is the Pythagorean Theorem? Toolbox: In a right triangle, each of the sides forming the right angle is a leg. The side opposite the right angle is the hypotenuse, which is also the longest side. The Pythagorean Theorem: In 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. a² + b² = c² a c b

An if-then statement is called a conditional. The part following the “if” is the hypothesis, and the part following the “then” is the conclusion. The converse of a conditional switches the hypothesis and the conclusion, which may or may not give a true statement. The Converse of the Pythagorean Theorem: If a triangle has sides of lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle with hypotenuse of length c. You can use the converse of the Pythagorean Theorem to determine whether a triangle is a right triangle.

What is the length of the hypotenuse of this triangle? ALGEBRA 1 LESSON 11-2 a 2 + b 2 = c 2 Use the Pythagorean Theorem = c 2 Substitute 8 for a and 15 for b = c 2 Simplify. 289 = c 2 Find the principal square root of each side. 17 = c Simplify. The length of the hypotenuse is 17 m. 11-2

A toy fire truck is near a toy building on a table such that the base of the ladder is 13 cm from the building. The ladder is extended 28 cm to the building. How high above the table is the top of the ladder? ALGEBRA 1 LESSON 11-2 Define:Let b = height (in cm) of the ladder from a point 9 cm above the table. Relate:The triangle formed is a right triangle. Use the Pythagorean Theorem. 11-2

ALGEBRA 1 LESSON 11-2 Write: a 2 + b 2 = c b 2 = 28 2 Substitute b 2 = 784Simplify. b 2 = 615Subtract 169 from each side. b 2 = 615Find the principal square root of each side. b 24.8Use a calculator and round to the nearest tenth. (continued) The height to the top of the ladder is 9 cm higher than 24.8 cm, so it is about 33.8 cm from the table. 11-2

Determine whether the given lengths are sides of a right triangle. ALGEBRA 1 LESSON 11-2 a. 5 in., 5 in., and 7 in. This triangle is not a right triangle. b. 10 cm, 24 cm, and 26 cm This triangle is a right triangle Simplify. 676 = Determine whether a 2 + b 2 = c 2, where c is the longest side Determine whether a 2 + b 2 = c 2, where c is the longest side Simplify. 50 = 49 / 11-2

ALGEBRA 1 LESSON 11-2 If two forces pull at right angles to each other, the resultant force is represented as the diagonal of a rectangle, as shown in the diagram. The diagonal forms a right triangle with two of the perpendicular sides of the rectangle. For a 50–lb force and a 120–lb force, the resultant force is 130 lb. Are the forces pulling at right angles to each other? 16,900 = 16,900 The forces of 50 lb and 120 lb are pulling at right angles to each other Determine whether a 2 + b 2 = c 2 where c is the greatest force ,400 16,

1.Find the missing length2.Find the missing lengthto the nearest tenth. 3.A triangle has sides of lengths 12 in., 14 in., and 16 in. Is the triangle a right triangle? 4.A triangular flag is attached to a post. The bottom of the flag is 48 in. above the ground. How far from the ground is the top of the flag? no 57 in. When you are finished, read pg and complete problems #1 – 5, Turn in all 12 problems.

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