Among people who can admit they liked math, there are usually two camps: those who preferred algebra, and those who preferred geometry. I am 100% in the former category. I still have my high school geometry notebook, in which two of my pals and I wrote our own theorems about how Pythagoras was in alliance with the devil. However, teaching for Kaplan has taught me something very important about geometry:
Circles are your friends.
Triangles and quadrilaterals are OK, too, but circles are your friends because EVERYTHING you need to know will be given to you. A GED problem may give you a triangle or a square inside a circle, which makes many test-takers cringe, but the only reason the circle is there is to help you!
All circles have a golden ratio, and you only need to know one piece of information to find out everything you need to know. Here it is:
|
the measure of an interior (center) angle |
: |
360 (the measure of the circle) |
|
the area of the sector formed by that angle |
: |
π r2 (the area of the circle) |
|
the length of an arc formed by that angle |
: |
2πr (the circumference of the circle) |
So if you know the center angle is 90°, you can put it in the ratio and determine that everything you need to know about this circle fits the 90:360, or 1:4, ratio. The area of the sector — the slice of pie the angle carves out — will be 1/4 the area of the circle, and the length of the arc — the curved edge of the pie slice — will be 1/4 the circumference of the circle.
Of course, you can also use the circumference or the area to solve for r and identify the radius, which will help you determine lengths and ratios of any other shapes drawn in, on, or around a circle in a GED math problem. Pretty sweet, huh?
