Understanding Relationships and Establishing Patterns Will Help Us Measure and Define Physical Space

__Exterior Angle Investigation:__

*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.*