 Since the pythagorean relationship is true for all right triangles, we can write an algebraic equation to describe it: c² = a² + b² In the triangle to the right, the hypotenuse has length “c”, and the legs have lengths “a” and “b”. The area of the square on the hypotenuse is c x c, or c². The areas of the squares on the legs are a x a and b x b, or a² and b². Since the sum of the areas of the smaller leg squares equal the area of the hypotenuse square, we can say c² = a² + b².

 Watch the following video. Is the scarecrow correct with his review of the Pythagorean Theorem? Is Homer correct with his review of the Pythagorean Theorem?  Pythagorean Theorem: The Scarecrow Pythagorean Theorem: The Scarecrow  Pythagorean Theorem: Homer Simpson Pythagorean Theorem: Homer Simpson

 Using what you now know about the pythagorean relationship, solve this problem:  A doorway is 2.0m high and 1.0m wide. A square piece of plywood has side length of 2.2m. Can the plywood fit through the door? How do you know? Show your work.

 Answer: The height of the doorway and the width is too small for the plywood to fit. Only other option is diagonally. I need to find the length diagonally between one corner to the next of the doorway. I will draw a diagram. To find the length of the diagonal, I will draw a line from corner to corner. Now I have 2 right angled triangles. The diagonal represents the hypotenuse. I can use the pathagorean equation to find the diagonal. I select one right triangle to solve, and place the numbers into the equation c² = a² + b². Based on my calculations, the square piece of plywood should be able to fit since the diagonal of the doorway is 2.24m in length. 1.0m 2.0m ? c² = a² + b² c² = 2² + 1² c² = c² = 5 c = √5 c = 2.24m

 With a partner, solve the different problems posted around the room. Remember to draw diagrams to help you, and show your work.