1. Pythagorean Theorem

2. Bell Work □ Please graph the problem and the answer: 9² + 12² = □ Graph the problem on one paper and the answer on the other paper. See my Example on the board.

3. Pythagorean Theorem - □ In right triangles, the square of the length of the hypotenuse is equal to the sum of the squares of its legs. □ a² + b² = c²

4. Right Triangle □right triangle –triangle that has one right angle □leg – the two sides of a right triangle that form a right angle □right angle – an angle that measures 90º □hypotenuse – the side of a right triangle that is opposite the right angle; the longest side of a right triangle

5. hypotenuse leg right angle 90°

6. Who can find the Right Triangles?

7. Is the triangle Right? Using the Pythagorean Theorem, determine which of the following would be right triangle. a.18 feet, 24 feet, 30 feet b.3 miles, 4 miles, 5 miles c.11 inches, 13 inches, 17 inches

8. Converse □If you reverse the parts of the Pythagorean Theorem, you have formed its converse. The converse of the Pythagorean Theorem is also true. □ EX: c² = a² + b² □if the sides of a triangle have lengths a, b and c so that c² = a² + b², then the triangle is a right triangle.

9. Example: □ The hypotenuse of a right triangle is 15 feet and leg a is 12 feet. What is the length of leg b?

10. Pythagorean Triples □ A set of three integers that satisfy the Pythagorean Theorem. abcCheck a² + b² = c² original3459 + 16 = 25 x2681036 + 64 = 100 x39121581 + 144 = 225 x4121620144 + 256 = 400 x5152025225 + 400 = 625

11. Who uses the Pythagorean Theorem? □ Cartographers (map makers) □ Surveyors □ Designers □ Architects □ Pilots □ Sailors □ Astronomers □ Astronauts □ Construction Workers □ Oceanographers

12. Do I use the Pythagorean Theorem? □ Which path is the quickest? 1 mile 2 miles 1 mile