Final Project
Description
Alexis Magallanes and Jenna McCollum
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
triangle to move and see how the areas of the pentagons change. We then
form the relationship that the areas of both pentagons a^2 and b^2 are
equal to the area of pentagon c^2. The main way this investigation is
different from paper and pencil is that it enables us to demonstrate
what exactly we are calculating when using the theorem. Geogebra also
allows students to play with different shapes without having to draw out
a ton of examples by hand. We first used a segment then a hemisphere to create our
right triangle .Then by using the parallel lines tool, and the circle
through center of point tool, we created the polygons on the outside of
the triangle. Our pentagon on line C would not face downward the way we
wanted it, so we used the Reflect about line tool to get it to flip
downward. We also used the Latex formula and symbols to show how each
variable changes algebraically when moving a point on the triangle. For
the more visual learners we used the translate by vectors tool to move
down the pentagons, in order for us to show the students how pentagons
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
(pythagorean theorem). We also used MP 5 because the bottom is a good way
for visual learners to compare what we learned about the equation, to
what is happening when the areas of the pentagons change.