Magoosh and Manhattan 5lb. Book Review: Triangles

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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, side2+side2 = hypotenuse2 — 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 [42 – 32] 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.

Sonjiala Jackson-Hotchkiss

Sonjiala (SON-ja-la) is currently pursuing an MS degree in chemistry at UC San Diego. As a member of the Bridges to Baccalaureate Program at San Diego Mesa College, her research in organic chemistry includes the synthesis of fatty acid esters of vitamin C that will be tested for their ability to inhibit glycolytic enzymes. In an additional research project she uses analytical chemistry techniques to determine the composition of World War II era California pottery.

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