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Kyle ShelleyMike IsaacsonBrad PerryLara HunsakerPythagorean Theorem: Discover-a-Relationship LessonObjective: Students will be able to discover the relationship (Pythagorean Theorem) between the sides of a right triangle from the squares derived from the lengths of the sides of the triangle.Standard: Prove theorems involving similarity4. Prove theorems about triangles. Theorems include: a line parallel to oneside of a triangle divides the other two proportionally, and conversely; thePythagorean Theorem proved using triangle similarity.Materials: Poster Board, rulers, markers, scissors, notebook, pencil, calculatorActivity Plan:Experimenting: Split students into groups. Have students cut out three triangles, an obtuse (red), a right (green), and an acute (blue) triangle from the poster board. Now instruct the students to create squares of the same color. The side lengths of the squares should equal one side of a triangle. There should be a total of 9 squares. Have the students try to manipulate the area of two of the squares into the area of the last square (students are free to cut their squares into any shape as long as they use the entire square). Reflecting and Explaining: Students will fill out the worksheet given as they reflect on this experiment. Have each group choose a spokesman to share with the class what their group discovered.Hypothesizing and Articulating: As a class determine any relationships. Hypothesize a general form (a2+b2=c2).Verifying and Refining: Have the students take their triangles and measure each side. Have them apply the Pythagorean Theorem (or whatever the class the class calls it at this point) to each triangle to prove their hypothesizes true or false. (Students might hypothesize that: two of the squares from the acute and obtuse triangles won’t equal the other square from each triangle, the right triangle’s side squares add up to the hypotenuse’s square, etc.)Note: Make sure that the class realizes that it only works for right triangles.BEHOLD! A mini-lesson on the Pythagoreans.Triangle Task SheetName________________________As a group get one sheet of each color poster board. Create three triangles, one acute, one obtuse and one right triangle, from the poster board. Do make them huge because you will need lots of left over poster board. Now, measure one side of the acute triangle. Create a square using the length you got from measuring the side of the triangle. Repeat this step for all remaining sides of all the triangles.Take two of the squares you created from one of the triangles and try to make the area of the squares fit exactly into the remaining square. Write down in your observations in the spaces below. Do this for all of the triangles and their corresponding squares. Remember that you can cut the two squares in any shape you want to make everything fit but there can be no overlapping on the third square. Organize your thoughts and hypothesizes about your work with acute triangles and their corresponding anize your thoughts and hypothesizes about your work with right triangles and their corresponding anize your thoughts and hypothesizes about your work with obtuse triangles and their corresponding squares.Make a hypothesis about the relationship of the squares of the given triangles. Mini-experiment:Prompt: For which type of triangle is the Pythagorean Theorem applicable? Why? Drawings are encouraged with explanation.+1 for stating that the Pythagorean Theorem is only for Right Triangles.+1 for an explanation of why, i.e. prove the theorem. ................
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