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Today in class we concluded our discussion on the buried treasure. Our conversation quickly turned into the topic of angles, and what an angle is. We had many debates and different conclussions as to what an angle is. We created 2 right triangles, 45, 45, 90 degree angels. We stated that 90 degrees is also perpendicular, and 1/4 of a circle. But what is a circle? These were the types of questions asked one after another.

Our end result for the day, we stated an angle to be "the space between two rays whose endpoints coincide"

some angels are in triangles, or some other shape and those seem to be finite.

As a class we realized how we have to many ways and words to describe what an angle might be and how each one of those words play off of each other. This is my understanding as to why we are in this class to begin with. To answer the so called "obvious" questions we assume to just know.

At the end of class we had an assignment to complete with a partner...

Lab: -- throughout please provide a definition of every term we used. 1.Construct equilateral tiragle using geogebra. 2.Discuss all the things you have done that may require a proof, discuss the proofs. 3. Is every equilateral triangle also equiangular? 4. Use this construction to construct a regular hexagon. 5. Tile the plane with regular triangles (solid lines) and regualr hexagons (dashed lines). Basically reporduce the picture. 6. Consruct a square. = Image found in lab work!!! =  The statement about angles being "within" a triangle or another shape as being finite, can we for sure conclude that the angle is indeed finite? As discussed whether the angle is "within" a triangle or not it still remains to be the same angle. Also, I don’t believe the angle could be finite if we refer to an angle as we defined it on Wednesday as “the space between two rays whose endpoints coincide”. Although you did mention a reason why we are discussing all of these definitions and terms I remember it being stated in class that by questioning what we are doing in this class we are learning how to answer the "why's" not just the "whats". This is important and extremely necessary in the field of mathematics. A huge problem that we had in deciding what an angle was using measurements in the definition. It really shows that what we learned in elementary and middle school about geometry might not have given us a full understanding of the concepts that we think we know. We spent so much time trying to define something as simple as an angle and yet I would say that most of us thought we had a grasp on the definition years ago.