MATH 329 Productive Failure- Two

Misconception/ Reflection of Error:

When originally solving this problem I had not yet seen a problem like this since my group did not get to these kind of problems in the workbook the day before. Due to the "new" type of question, I began to panic a little, not recognizing the extremely simple solution to the problem. I knew similar triangles had to have corresponding angles that were equal to one another and proportional side lengths and since both angles given for each of the triangles compared were not equal to one another, I wrote that none of the triangles were similar. However, after turning the quiz in and talking with classmates, I quickly realized that finding the third missing angle of the compared triangles is extremely simple. Since we know the interior angles of a triangle add up to 180, all we have to do when given only two angles is add the two angles up and then subtract the sum from 180 to get the missing third angle.

Once realizing this, finding the missing third angles and comparing the two triangles given in parts A, B, and C, was extremely simple and I was able to find that triangle A and triangle B actually indeed are similar.

Reflecting back on this error, I realize that the steps taken are sometimes much simpler than we originally think. From this, I have learned that even if I have not seen a problem before, prior knowledge can very well aid in figuring out how to solve the problem.