Geometry : The Pythagorean Theorem

1. Geometry: The Pythagorean Theorem

2. Pythagorean Theorem • A formula named after the Greek mathematician Pythagoras is used. • right triangle Hover on the links, then click Next button

3. Attic of house Houston Astros’ Minute Maid Park Sailboat Kite Flying Aerial view of field on a farm Click on a hyperlink to learn more about Pythagorean Theorem and triangles.

4. About Triangles and Sailboats Sailboat Triangle Hover on the links to read about the similarities between the diagrams. Now, click on Triangle.

5. Example 1 C 2 = A 2 + B 2 Question: Find the length of the hypotenuse of a right triangle, if a = 12 and b = 5.

6. Answer: C 2 = A 2 + B 2 C 2 = 12 2 + 5 2 C 2 = 144 + 25 C 2 = 169 C = √169 C = ± 13 C 5 12 The length of the hypotenuse is 13 units.

7. Know Your Sailboats the Real World Use of the wind is one of the oldest forms of powering a vessel. Sailboats range in size and complexity, but all have basically the same four components. • The hullcarries the passengers and supports the rigging. • The rigging includes many parts of the sailboat, such as the lines (sheetsand halyards), mainsail, headsail (jib), boom, and mast. • The keel or centerboard is attached to the bottom of the hull and keeps the boat from sliding sideways through the water. • The rudderis used to steer the sailboat, turned by a tiller or steering wheel. Question: Match the legs of a triangle with the parts of a sailboat.

8. Answer: B = boom A = mast Click on Return or Previous button to view more real life problems.

9. Trapezoid Example Question: Look at the trapezoid below. Find the missing leg. Question: Find the length of the missing legs.

10. Answer: C 2 = A 2 + B 2 C 2 = 8 2 + 3 2 C 2 = 64 + 9 C = √ 73 The length of the hypotenuse is √ 73.

11. Real World Attic without ProperInsulation Question: Find and then label the triangle. Next, if a = 9 and b = 12, find the missing leg. Click the Next button to see if you got the correct answer.

12. Answer: C 2 = A 2 + B 2 C 2 = 9 2 + 12 2 C 2 = 81 + 144 C 2 = 225 √ C = √ 225 C = 15 The length of the hypotenuse is 15.

13. Diamond - Triangle Example Question: Find leg b if leg a = 3 and c = 5. Click on the Next button to find the answer.

14. Answer: C 2 = A 2 + B 2 5 2 = 3 2 + B 2 25 = 9 + B 2 25 - 9 = B 2 √ 16 = √ B 2 4 = B The length of Leg B is 4 units.

15. Houston Astro’s Baseball Diamond Question: A baseball scout uses many different test to determine whether or not to draft a particular player. One test is how quickly he can throw the ball from home plate to second base. On a baseball diamond, the distance from one base to the next is 90 feet. What is the distance from home plate to second base? Click the Next button to see the answer.

16. Answer: C 2 = A 2 + B 2 C 2 = 90 2 + 90 2 C 2 = 8100 + 8100 √ C 2 = √16200 C = 127.28 feet There is a distance of ~127 feet from the home plate to second base on a baseball diamond.

17. Isosceles Triangle Example Question: Find the length of the missing side. Let b = 5, and c = 15. Click the Next button to see if you answered correctly.

18. Answer: C 2 = A 2 + B 2 15 2 = a 2 + 5 2 225 = a 2 + 25 √ 200 = √ a 2 14 = a The length of Leg a is 14 units.

19. Real World Isosceles Triangle Find the missing leg

20. Instructions in drawing Poom Khao Bin Design 1. Draw a square like a kite. Please see the shape, size and other detail in the example.2. When the outline is completed, draw two inner pictures shape like two drops of water. The smaller one must have lighten colour than the outer one.3. Draw the outline of the outer petals lightly.4. Draw the outer petals in details. All petals must be stuck with the outer "drop of water". Begin with the left and the right petals. The instructions in drawing the four petals are similar to those of Krajang Ta Oil. The difference is that in this case, we draw only half of the design. Sometimes the real beauty of math is in the design. Enjoy this piece of jewelry or design. Answer: c 2 = a 2 + b 2 = 2 2 + .7 2 = 4 + .49 C = √4.49

21. Quadrilateral Triangle Example 32 26 10 Question: Let a = 32 – 10, and b = 26. Find c. Click on the Next button for answer.

22. Answer: c 2 = a 2 + b 2 = ( 32 - 10 ) 2 + 26 2 = 22 2 + 26 2 = 484 + 676 = 1160 C = 34.06 The c side of the “field” is ~34.06 meters

23. Real World Example of a Quadrilateral- a Farm Field Question: Which field is most likely an example of a quadrilateral? Click on the Next button for the answer.

24. Answer: Field 2 is shaped most like a quadrilateral. You must be able to visualize and manipulate the legs of the triangle, and understand the Pythagorean Theorem concept to solve this problem.

25. Teks • §111.36. Mathematical Models with Applications • c) Knowledge and skills. • The student uses a variety of strategies and approaches to solve both routine and non-routine problems. The student is expected to: (A) compare and analyze various methods for solving a real-life problem; • (B) use multiple approaches (algebraic, graphical, and geometric methods) to solve problems from a variety of disciplines; and • (C) select a method to solve a problem, defend the method, and justify the reasonableness of