Triangles, triangles, triangles!
It’s no secret that most students aren’t massive fans of the geometry questions on the SAT math. And why would they be? If you’re taking your SAT your junior or senior year, in all likelihood you haven’t thought about geometry in awhile… and reviewing a ton of formulas about shapes isn’t too many students’ idea of a good time.
But, contrary to how it might feel, the geometry questions are your friends. The majority of SAT geometry questions are extremely simple, and mostly revolve around triangles, circles, and quadrilaterals (squares, rectangles, etc).
Here are some simple tips for dealing with the SATs most common geometric shape, the triangle!
Get those formulas down.
Rule of 180: The sum of interior angles of a triangle equals 180 degrees. (In layman’s terms: add up all three angles, and you’ll get 180.)
Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are the legs of a right triangle and c is the hypotenuse.
Area of a triangle: (1/2)(base)(height). Keep in mind that the base and height are perpendicular to each other.
The base and height for an isosceles right triangle are the same.
Oftentimes the SAT will try and fool you by giving you the area of an isosceles right triangle and asking for the height. Don’t give up! Remember that for an isosceles right triangle, base and height are the same — which means that if the area of the triangle is 12, we can find the side of the triangle by using the formula 12 = (1/2)(b^2).
Split an equilateral triangle into two 30-60-90 triangles.
This is a big one. If you’re doing a difficult triangle problem that involves an equilateral triangle, consider splitting it down the middle! Particularly in triangle problems that involve equilateral triangles and area, splitting the original triangle often makes it considerably easier to find the height… which makes it considerably easier to rack up the points.
Remember that all special right triangles are printed in the front of your exam booklet.
This means there is no excuse for missing a special right triangle problem–you don’t even need to memorize the rules! All you need to do is be able to recognize a special right triangle. Keep in mind that any isosceles right triangle is 45-45-90, and that if you see a 30 degree or 60 degree angle on a right triangle, it’s a 30-60-90.
Don’t be afraid to double-check! The formulas printed in the beginning of the book are there to help you.
Remember that variables are just numbers.
Supplementary angles add up to 180. So if one angle is 80 degrees, the other is 100. Seems easy enough, right?
On the SAT, difficult triangle questions will oftentimes have you finding the supplementary angle of a variable instead of a number. Don’t let this confuse you! The supplementary angle of z is (180 – z). The supplementary angle of (m + n) is (180 – [m + n]). Variables are numbers too!
Always write your equations down.
It seems silly, but writing down your equations can be extremely helpful. If you’re stuck, writing down something as simple as the area formula can give you a place to start, and get your brain going!
What other tricks do you use to tackle triangles? Leave your best tips in the comments below!