Understanding Relationships and Establishing Patterns Will Help Us Measure and Define Physical Space
Exterior Angle Investigation:Did the question and directions in the investigation make sense when you were doing it or did you need help clarifying what to do? Did you get stuck along the way, or make any mistakes that had to be corrected?
The day I got this worksheet, I was in class having a chat with my friends. I wasn't focusing on what I was doing, and I only half-completed the work sheet then. When I got home, I looked over what I had done, and noticed everything was wrong! Even though this wasn't a lot of work, I had to erase everything and start again. Once I did it again, I checked with my mom and she said I had gotten all my answers correct!
Explain the pattern or special relationship that you found and explain how the responds to the guiding statement: "Understanding relationships and establishing patterns will help us measure and define physical space." Be clear. Feel free to paste in images to really demonstrate what you are explaining. This is your opportunity to explain what you understand about this topic.
Throughout this investigation, I discovered that angles <C + <D = 180 degrees. Before I did this investigation, I already knew that angles <A + <B + <C = 180 degrees as well. Because I knew that <C + <D also equaled to 180 degrees, I next discovered that angles <A + <B = <D. Now I had a shortcut to finding a missing angle, by using both the exterior and the interior angle(s).
For example, in question 1 on the worksheet, I had to find the exterior angle. I solved the problem by first using finding out angles <A and <C. Angle <A was easy to discover, since it was simply a right angle (90 degrees). Then I added angle <A + <B = 130 degrees. I then subtracted 180 - 130 degrees = 50 degrees (angle <C). Finally, to find the exterior angle, the interior and exterior have to add up to 180 degrees. Looking back at what I had already figured out, I then realised that angles <A + <B = <D, so <D was 130 degrees.
I can now conclude that using the relationships (angles <A + <B = 180 degrees, <C + <D = 180 degrees, <A + <B = <D) helped me find the pattern between the three questions that I completed on the worksheet. Now that I know the pattern, throughout my geometry career I can easily find and be able to measure a missing angle which leads me to having the ability to defining physical space.
Create a math problem that could be used on a test that uses the concept you are explaining in a problem solving situation. It could be a word problem, or a diagram with unknown angles, etc. Try to imagine how this concept could be applied to a real life situation, and how it could be tested on an exam.
Percy and Audrey were trying to find the missing angles. Who was right? If so, why?
Answer: Percy and Audrey were both right. Percy just solved the problem in a different way.