Alexis Magallanes and Jenna McCollum[br]The goal of our presentation was to create a sketch that would look more into the pythagorean theorem and explore what happens to the pentagons when we move a point on the right triangle. The basic sketch works like this: choose a point on the [br]triangle to move and see how the areas of the pentagons change. We then [br]form the relationship that the areas of both pentagons a^2 and b^2 are [br]equal to the area of pentagon c^2. The main way this investigation is [br]different from paper and pencil is that it enables us to demonstrate [br]what exactly we are calculating when using the theorem. Geogebra also [br]allows students to play with different shapes without having to draw out[br] a ton of examples by hand. We first used a segment then a hemisphere to create our [br]right triangle .Then by using the parallel lines tool, and the circle [br]through center of point tool, we created the polygons on the outside of [br]the triangle. Our pentagon on line C would not face downward the way we [br]wanted it, so we used the Reflect about line tool to get it to flip [br]downward. We also used the Latex formula and symbols to show how each [br]variable changes algebraically when moving a point on the triangle. For[br] the more visual learners we used the translate by vectors tool to move [br]down the pentagons, in order for us to show the students how pentagons [br]a^2+b^2=pentagon c^2 and see how they increase and decrease in size. It also shows how pentagon c^2 stays the same when only moving points a and b. We thought of MP 4 when creating our project because it allows us to use our prior knowledge (areas of the polygons we choose) and then apply it to the equation we are learning [br](pythagorean theorem). We also used MP 5 because the bottom is a good way[br] for visual learners to compare what we learned about the equation, to [br]what is happening when the areas of the pentagons change.
