In math, we started a new unit on geometry, and the study of angles. At first, I was really excited, since I am good at angles. However, after hearing what we were going to learn, I was lost. Now, if I look back, I think that I have learned so much. Not only have I learned about angles, but about relationships between angles. I never thought one depended on another, unless it was a triangle in where all the angles added up to 180. I find relationships between angles the only way I can solve these new problems.
Understanding relationships and establishing patterns will help us measure and define physical space.
Investigation: Exterior Angle Investigation
I think that it all went smoothly. I understood most of the work by myself, however, at the end, I needed some clarifying. I understood the formula, and the whole conclusion. The only thing I was lost in was the “why” part. Mr. Hancock helped me on that one, but overall, I think I understood the concept.
The pattern I found was that A+B=D
This is because all angles in a triangle add up to 180 (<A, <B, and <C), as well as supplementary angles(<C and <D). 180- <C = <A and <B, and since <C is supplementary to <D, 180-<C= <D as well. That means they could both substitute each other.
If we develop a high level of understanding of these patterns and relationships, we will be able to find out the measurement of the angles. If we knew the measurements of <A and <B, by understanding these relationships, it would facilitate finding the measurement of <C and <D. The way to solve that would be: Since we know that <A+<B=<D, we would do that. With <D, we would do 180-<D, resulting in finding the measurement of angle C.
Elizabeth’s room is shaped like a triangle. Outside her room, she wants to place a fire place, but needs to know the angle. This is how it looks:
If the two congruent angles are 72, what would be the angle of the fire place?
Investigation: Polygon Interior Angle Investigation
I find this worksheet the hardest. I understood everything, just struggled to find a way to put my work into a formula. I think that the more I did, the harder it started to get. However, it was ok. I did go to Mr. Hancock for help sometimes, but otherwise I think I understand this work.
The formula that really helped me was (number of sides - 2) * 180
Because I established this, it was easier to keep on going. I used that as my base, and kept building off of that. For example, once I knew that all of the angles in the polygon (interior) were equal, I thought division. So I used the base (number of sides - 2) * 180 and added /number of sides. Then it got tricky; how to find the exterior angle. What I did was add in a line to make one of the angles of the shape supplementary to the "outer" one. Once I found out the value of those two, I took the outer one and added 180. That is how I found out the value of the exterior angle. However, I am still not so sure about my formula. That is something I need to improve on.
How does this relate to the leading question? I used the base relationship to find out the other angles.
What is the measurement of the outer angle in a hexagon?
Laura,
ReplyDeleteI can see you put a lot of thought and clarity into it. However instead of saying putting outer angle I would put exterior angle, so the audience won't get confused. Also, if you put a picture of a Hexagon for the question in the end it would be more visually appealing. With exception of those minor errors, I would give you a 7 or more, if there is such a grade.