I found the Magoosh videos on triangles provided impressive preparation for working the problems in the Manhattan 5lb Book. I glanced through the chapter on triangles in the Manhattan 5lb Book before watching the videos. While I could work some of the problems immediately, I found enough of them to be unfamiliar that I didn’t break out pencil and paper. Instead I went to the Magoosh videos for a review of triangles.

There are five Magoosh videos dedicated to triangles in their Geometry section including lessons on isosceles, equilateral, right, and special right triangles. I was conversant in the basics regarding triangles — three sides, angles sum to 180, and so on. I was also familiar with common considerations regarding right triangles and similar triangles as I used these concepts in my physics classes. Still the videos reacquainted me with details that allowed me to work problems faster and with more confidence.

I worked problems from the triangle chapter in the Manhattan 5lb Book shortly after using Magoosh triangle videos for review. I was surprised by how easily and quickly I tore through the problems. One of the problems I missed incorporated a pitfall that I had been explicitly warned about in a video.

The problem had to do the lengths of the sides of right triangles. With right triangles, side^{2}+side^{2} = hypotenuse^{2} — the Pythagorean Theorem. The trap had to do with Pythagorean triplets — groups of three side lengths that satisfy the Pythagorean Theorem [e.g., (3,4,5), (5,12,13)]. In the problem, the lengths of two sides were given, and I had to determine the third side for a quantitative comparison. I saw 3 and 4 and thought 5. The catch is that the question did not state that 3 and 4 were leg lengths, and the unknown length was the hypotenuse. In the given question, 4 was the length of the hypotenuse (the longest side) and the missing length was a leg. So the solution then was not 5 but sqrt [4^{2} – 3^{2}] or sqrt [7]. Given the warning about this very trap in the Magoosh videos, I was surprised by how quickly and mindlessly I fell for it when in a rush.

My mistake punctuated the importance of working problems contemporaneously with watching videos.