Lesson 2 Menu 1.Find the geometric mean between the numbers 9 and 13. State the answer to the nearest tenth. 2.Find the geometric mean between the numbers.

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Presentation transcript:

Lesson 2 Menu 1.Find the geometric mean between the numbers 9 and 13. State the answer to the nearest tenth. 2.Find the geometric mean between the numbers State the answer to the nearest tenth. 3.Find the altitude of the triangle shown in the figure. 4.Refer to the figure. Find x, y, and z.

Lesson 2 MI/Vocab Pythagorean triple Use the Pythagorean Theorem. Use the converse of the Pythagorean Theorem.

Lesson 2 TH1

Lesson 2 Ex1 LONGITUDE AND LATITUDE Carson City, Nevada, is located at about 120 degrees longitude and 39 degrees latitude. NASA Ames is located about 122 degrees longitude and 37 degrees latitude. Use the lines of longitude and latitude to find the degree distance to the nearest tenth of a degree if you were to travel directly from NASA Ames to Carson City. Find the Length of the Hypotenuse

Lesson 2 Ex1 Find the Length of the Hypotenuse Use the Pythagorean Theorem to find the distance in degrees from NASA Ames to Carson City, represented by c. The change in latitude is or 2 degrees latitude. Let this distance be b. The change in longitude between NASA Ames and Carson City is or 2 degrees. Let this distance be a.

Lesson 2 Ex1 Answer: The degree distance between NASA Ames and Carson City is about 2.8 degrees. Find the Length of the Hypotenuse Pythagorean Theorem Simplify. Add. Take the positive square root of each side. Use a calculator.

A.A B.B C.C D.D Lesson 2 CYP1 A.about 5.8 degrees B.about 8.5 degrees C.about 10 degrees D.about 12.5 degrees LONGITUDE AND LATITUDE Carson City, Nevada, is located at about 120 degrees longitude and 39 degrees latitude. NASA Dryden is located about 117 degrees longitude and 34 degrees latitude. Use the lines of longitude and latitude to find the degree distance to the nearest tenth of a degree if you were to travel directly from NASA Dryden to Carson City.

Lesson 2 Ex2 Find the Length of a Leg Find d.

Lesson 2 Ex2 Find the Length of a Leg Answer: d ≈ 5.2 cm Pythagorean Theorem Simplify. Subtract 9 from each side. Take the positive square root of each side. Use a calculator.

Lesson 2 CYP2 1.A 2.B 3.C 4.D A.17 B.12.7 C.11.5 D.13.2 Find x. Round your answer to the nearest tenth.

Lesson 2 TH2

Lesson 2 Ex3 Verify a Triangle is a Right Triangle COORDINATE GEOMETRY Verify that ΔABC is a right triangle.

Lesson 2 Ex3 Verify a Triangle is a Right Triangle Use the Distance Formula to determine the lengths of the sides. Subtract. Simplify. Subtract. Simplify.

Lesson 2 Ex3 Verify a Triangle is a Right Triangle 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.

Lesson 2 Ex3 Verify a Triangle is a Right Triangle Answer: Since the sum of the squares of two sides equals the square of the longest side, ΔABC is a right triangle. Converse of the Pythagorean Theorem Simplify. Add.

Lesson 2 Ex4 A. Determine whether 9, 12, and 15 are the sides of a right triangle. Then state whether they form a Pythagorean triple. Pythagorean Triples 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.

Lesson 2 Ex4 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. Pythagorean Triples

Lesson 2 Ex4 Pythagorean Triples B. Determine whether 4, and 8 are the sides of a right triangle. Then state whether they form a Pythagorean triple. Pythagorean Theorem Simplify. Add. Answer: The segments form the sides of a right triangle, but the measures do not form a Pythagorean triple.

A.A B.B C.C D.D Lesson 2 CYP4 A.Yes, the segments form a right triangle, and the measures form a Pythagorean triple. B.Yes, the segments form a right triangle, but the measures do not form a Pythagorean triple. C.No, the segments do not form a right triangle, but the measures do form a Pythagorean triple. D.No, the segments do not form a right triangle, and the measures do form a Pythagorean triple. A. Determine whether 6, 8, 10 are the sides of a right triangle. Then state whether they form a Pythagorean triple.

A.A B.B C.C D.D Lesson 2 CYP4 A.Yes, the segments form a right triangle, and the measures form a Pythagorean triple. B.Yes, the segments form a right triangle, but the measures do not form a Pythagorean triple. C.No, the segments do not form a right triangle, but the measures do form a Pythagorean triple. D.No, the segments do not form a right triangle, and the measures do form a Pythagorean triple. B. Determine whether 5, 8, 9 are the sides of a right triangle. Then state whether they form a Pythagorean triple.