1. 9/23/20155.4: The Pythagoream Theorem 5.4: The Pythagorean Theorem Expectation: G1.2.3: Know a proof of the Pythagorean Theorem and use the Pythagorean Theorem and its converse to solve multistep problems.

2. 9/23/20155.4: The Pythagoream Theorem Pythagorean Theorem In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the hypotenuse (a 2 + b 2 = c 2 ). a b c

3. 9/23/20155.4: The Pythagoream Theorem Informal Proof of the Pythagorean Theorem 3 4 5

4. 9/23/20155.4: The Pythagoream Theorem Determine the length of the third side of the triangles below. 32 24 65 25

5. 9/23/20155.4: The Pythagoream Theorem Members of the fire department lean a 26 foot ladder against a building. The side of the building is perpendicular to the level ground so that the base of the ladder is 10 feet away from the base of the building. To the nearest foot,, how far up the building does the ladder reach? A. 12 B. 15 C. 20 D. 22 E. 24

6. Square ABCD has a perimeter of 28 inches. How many inches long is diagonal AC? A. 7 B. 7√2 C. 7√3 D. 14 E. √14 9/23/20155.4: The Pythagoream Theorem

7. 9/23/20155.4: The Pythagoream Theorem Pythagorean Converse Theorem If the square of the longest side of a triangle is equal to the sum of the squares of the two shorter sides, then the triangle is a right triangle. If a 2 + b 2 = c 2, then the triangle is a right triangle.

8. 9/23/20155.4: The Pythagoream Theorem Pythagorean Triples Three numbers are a pythagorean triple if they satisfy the pythagorean converse theorem.

9. 9/23/20155.4: The Pythagoream Theorem Are the following numbers a Pythagorean triple? 35, 21, 28

10. 9/23/20155.4: The Pythagoream Theorem Pythagorean Inequalities Theorem For triangle ABC with c the length of the longest side: a. if c 2 = a 2 + b 2 then the triangle is a right triangle. b. if c 2 < a 2 + b 2 then the triangle is an acute triangle. c. if c 2 > a 2 + b 2 then the triangle is an obtuse triangle.

11. 9/23/20155.4: The Pythagoream Theorem A triangle has sides of 12 cm, 14 cm and 20 cm. Is the triangle acute, right or obtuse? acute Just kidding it is obtuse

12. 9/23/20155.4: The Pythagoream Theorem Assignment pages 326-329, #8-24 (evens), 26-29 (all), 34, 35, 40-42 (all)