Chapter 11, Section 2: Pythagorean Theorem

1. Warm Up: What is the sign of the product of two negative numbers? Find the Product or Sum: (-2) ² = (-6)² = 6² + 9² = 4² + 10² =

2. The Pythagorean Theorem Chapter 11, Section 2

3. Parts of Right Triangles The sides on either side of the right angle (90º) are called the LEGS The side adjacent to the right angle is called the HYPOTENUSE. The HYPOTENUSE of a Right Triangle Is always LONGER then the LEGS.

4. Pythagorean Theorem Use Pythagorean Theorem to determine any missing lengths of a RIGHT Triangle. A ² + B² = C² A and B are lengths of the LEGS. C is the length of the HYPOTENUSE. Another way: C = √A² + B²

5. Determine the Length of the Hypotenuse C ² = A² + B² C² = 6² + 8² C² = 36 + 64 C = √100 C = 10 8 cm 6 cm C cm Right Angle The legs are A and B for Pythagorean. A = 6 cm, B = 8 cm

6. Try These: Find the Missing Side Length of each Triangle Triangle 1 : Legs: 3ft and 4ft Triangle 2 : Leg: 12m; Hypotenuse: 15m

7. Find the value of X A ² + B² = C² 6² + x² = 9² 36 + x² = 81 X² = 45 X = √45 √ 45 = 6.7 (rounded) 9 in. 6 in. X in.

8. Use the Square Root Table to Approximate Square Roots In your book, page 746 has a whole table of square root solutions. Find the number in the N column, then find the answer in the √N column. Or use a calculator, just remember to round.

9. Identifying Right Triangles To see if a triangle IS a right triangle, plug the measurements into the Theorem. Sides: 12m, 15m, and 20m. Is this triangle a Right Triangle? A ² + B² = C², 12² + 15² = 20² ? 144 + 225 = ? 400 369 ≠ 400 The triangle with these measurements is NOT a right triangle.

10. Right ▲ or Not? Triangle 1: 7in, 8in, 9in? Triangle 2: 3m, 4m, 5m? Triangle 3: 5mm, 6mm, 10mm?

11. Assignment #31 Pages 567-568: 10-32 all.