Welcome to Interactive Chalkboard Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc.,

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Welcome to Interactive Chalkboard

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5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

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Welcome to Interactive Chalkboard Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc., Cincinnati, Ohio Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240

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Contents Lesson 7-1Geometric Mean Lesson 7-2The Pythagorean Theorem and Its Converse Lesson 7-3Special Right Triangles Lesson 7-4Trigonometry Lesson 7-5Angles of Elevation and Depression Lesson 7-6The Law of Sines Lesson 7-7The Law of Cosines

Lesson 2 Contents Example 1Find the Length of the Hypotenuse Example 2Find the Length of a Leg Example 3Verify a Triangle is a Right Triangle Example 4Pythagorean Triples

Example 2-3a COORDINATE GEOMETRY Verify that is a right triangle.

Example 2-3b Use the Distance Formula to determine the lengths of the sides. Subtract. Simplify. Subtract. Simplify.

Example 2-3c Subtract. Simplify. By the converse of the Pythagorean Theorem, if the sum of the squares of the measures of two sides of a triangle equals the square of the measure of the longest side, then the triangle is a right triangle.

Example 2-3d Converse of the Pythagorean Theorem Simplify. Add. Answer: Since the sum of the squares of two sides equals the square of the longest side, is a right triangle.

Example 2-3e COORDINATE GEOMETRY Verify that is a right triangle. Answer: is a right triangle because

Example 2-4a Determine whether 9, 12, and 5 are the sides of a right triangle. Then state whether they form a Pythagorean triple. Since the measure of the longest side is 15, 15 must be c. Let a and b be 9 and 12. Pythagorean Theorem Simplify. Add.

Example 2-4b Answer: These segments form the sides of a right triangle since they satisfy the Pythagorean Theorem. The measures are whole numbers and form a Pythagorean triple.

Example 2-4c Determine whether 21, 42, and 54 are the sides of a right triangle. Then state whether they form a Pythagorean triple. Pythagorean Theorem Simplify. Add. Answer: Since, segments with these measures cannot form a right triangle. Therefore, they do not form a Pythagorean triple.

Example 2-4d Pythagorean Theorem Simplify. Add. Determine whether 4, and 8 are the sides of a right triangle. Then state whether they form a Pythagorean triple. Answer: Since 64 = 64, segments with these measures form a right triangle. However, is not a whole number. Therefore, they do not form a Pythagorean triple.

Example 2-4e Answer: The segments form the sides of a right triangle and the measures form a Pythagorean triple. Answer: The segments do not form the sides of a right triangle, and the measures do not form a Pythagorean triple. Answer: The segments form the sides of a right triangle, but the measures do not form a Pythagorean triple. Determine whether each set of measures are the sides of a right triangle. Then state whether they form a Pythagorean triple. a. 6, 8, 10 b. 5, 8, 9 c.

End of Lesson 2

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