Last week, I made an activity for a geometry class using Geometer's Sketchpad. This is a tool anyone who teaches geometry should have in his or her classroom.
The topic of my activity was a proof of the Pythagorean theorem. It combined concepts of area, congruence, algebra, and construction. The construction of the inscribed squares was where I ran into trouble. I wasn't sure how to get the squares just right, so that they had the proper relationship and so that moving them around would keep the relationship stable. I never was able to make it so that students could manipulate the inner square, only the outer.
Anyway, it was disappointing that no where on the Internet is there an explanation of how to do this (without paying for it). In case anyone needs to do this, here is my (almost) perfect method. It will do.
First, construct a square in Geometer’s Sketchpad:
• Start with a line segment AB.
• Construct a perpendicular line m to your segment through A.
• Construct a perpendicular line n to your segment through B.
• Construct a circle with center B and second point at A.
• Mark one intersection of n with the circle as C.
• Construct line segment BC.
• Construct a circle with center A second point at B.
• Mark the appropriate intersection of the new circle with m as D.
• Construct segment AD.
• Construct segment CD.
• Hide the circles and the perpendicular lines.
Now, construct a square inscribed within your square ABCD:
• Construct the diagonals of square ABCD.
• Construct a circle with its center at the intersection of the square’s diagonals and its second point on AB, but closer to A than to B.
• Label the circle’s other intersection on AB (the one closer to B) as E.
• Construct a line segment from E to the point closest to C where your circle intersects BC.
• Label this point F.
• Construct a line segment from F to the point closest to D where your circle intersects CD.
• Label this point G.
• Construct a line segment from G to the point closest to A where your circle intersects AD.
• Label this point H.
• Construct line segment EH.
• Hide the circle, its center, its unlabeled point on AB, and the diagonals.
You now have a square inscribed within another square! Congrats!
2 comments:
hello, i dont know how i found your profile but im really hoping that you still use it. Im an aspiring mathematician. I really love math. Im 16 years old. And i really need some help with a math problem that ive been stuck in for over a week. It is for a math competition that I am in. If you can possibly help me you can find me on facebook. My name is Michael Rodriguez and I go to Mater Academy Charter High school in Miami FL. thank you in advance.
I'm so sorry, Mike! I didn't notice this comment until today. I really need to set it up so that I'm notified when people leave comments on my posts.
I'm currently using this for a class at U of I, and I just don't really go back and look at previous posts very often.
I hope you found someone to help you with the problem, or that you were able to solve it on your own. Keep up the interest in math! Aspiring mathematicians are rare and so important.
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