Part 1 and Part 2:

I constructed a square by using the "Angle with a Given Size" tool and making all 4 angles 90 degrees. I then used the "Polygon" tool to close the figure. I then labeled the sides to be able to show the students how the sides change as they move the points on the square in the applet. Here is a link to my construction on GeoGebraTube: http://www.geogebratube.org/student/m28683. This is the first time I used this program, so I had to play around with it __a lot__. I could not figure out why I could not move point C and D in my figure. Any advanced GeoGebra users out there that can figure out why? I am really interested in learning more about this software and how it works.

Question on Part 1:

Three ideas that students can learn from making a perfect square in GeoGebra is that all the angles are 90 degrees, the sides are congruent, and that all the exterior angles are the same. You can also have the students construct the diagonals of the square and then they will also be able to see that the diagonals are congruent and intersect to form a 90 degree angle, which makes the bisectors perpendicular lines.

Question on Part 2:

I found an applet that involves perpendicular lines and their slopes. Here is a link to the applet: http://www.geogebratube.org/student/m23016. This would be great for my Algebra 1 students when they are learning about this property in Chapter 5. It is easier for them to see how parallel lines have the same slope, but the opposite reciprocal slope of the perpendicular lines is harder to remember. This applet allows students to move the points on the perpendicular lines around and discover the relationship between the slopes of the two lines. If the students constructed the perpendicular lines themselves in this applet, they would also learn what points, lines, or measurements are important to include in the applet to be able to show the opposite reciprocal slopes and that the lines are perpendicular (showing the right angle the lines form). I think when students are put into the “creating” role, they learn so much more about the concept because they have to take into account everything needed to make each figure and label the necessary information to prove their point. I think that the creation step would have to be after the students have already learned and mastered the concept. This is a great challenging to enhance their understanding of the material!