5-Minute Check on Chapter 2 Transparency 3-1 5-Minute Check on Chapter 2 Evaluate 42 - |x - 7| if x = -3 Find 4.1  (-0.5) Simplify each expression 3. 8(-2c + 5) + 9c 4. (36d – 18) / (-9) A bag of lollipops has 10 red, 15 green, and 15 yellow lollipops. If one is chosen at random, what is the probability that it is not green? Which of the following is a true statement Standardized Test Practice: A 8/4 < 4/8 B -4/8 < -8/4 C -4/8 > -8/4 D -4/8 > 4/8 Click the mouse button or press the Space Bar to display the answers.

The Pythagorean Theorem Lesson 11-4 The Pythagorean Theorem

Click the mouse button or press the Space Bar to display the answers. Transparency 4

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Objectives Solve problems by using the Pythagorean Theorem Determine whether a triangle is a right triangle

Vocabulary hypotenuse – legs – Pythagorean triple – Corollary –

Pythagorean Theorem xxx

Pythagorean Triples A combination of three sides that satisfy the Pythagorean theorem and are all whole numbers (integers) Most common Pythagorean triples: 3-4-5 and multiples (6-8-10, 9-12-15, etc) 5-12-13 8-15-17 7-24-25

Example 1 Find the length of the hypotenuse of a right triangle if a = 18 and b = 24. Pythagorean Theorem and Simplify. Take the square root of each side. Use the positive value. Answer: The length of the hypotenuse is 30 units.

Example 2 Find the length of the missing side. In the triangle, and units. Pythagorean Theorem and Evaluate squares. Subtract 81 from each side. Use a calculator to evaluate . Use the positive value. Answer: To the nearest hundredth, the length of the leg is 13.23 units.

Example 3 Multiple-Choice Test Item What is the area of triangle XYZ? A 94 units2 B 128 units2 C 294 units2 D 588 units2 Read the Test Item The area of the triangle is A = ½ bh In a right triangle, the legs form the base and height of the triangle. Use the measures of the hypotenuse and the base to find the height of the triangle.

Example 3 cont Solve the Test Item Step 1 Check to see if the measurements of this triangle are a multiple of a common Pythagorean triple. The hypotenuse is units and the leg is units. This triangle is a multiple of a (3, 4, 5) triangle. The height of the triangle is 21 units. Step 2 Find the area of the triangle. A = ½bh Area of a triangle A = ½(28)(21) b = 28 and h = 21 Simplify. Answer: The area of the triangle is 294 square units. Choice C is correct.

Example 4a Determine whether the side measures of 7, 12, 15 form a right triangle. Since the measure of the longest side is 15, let , and Then determine whether Pythagorean Theorem and Multiply Add Answer: Since , the triangle is not a right triangle.

Example 4b Determine whether the side measures of 27, 36, 45 form a right triangle. Since the measure of the longest side is 45, let and Then determine whether Pythagorean Theorem and Multiply. Add. Answer: Since the triangle is a right triangle.

Summary & Homework Summary: Homework: If a and b are the measure of the legs of a right triangle and c is the measure of the hypotenuse, then c2 = a2 + b2 If a and b are the measure of the shorter sides of a triangle, c is the measure of the longest side, and c2 = a2 + b2, then the triangle is a right triangle Homework: pg