As we’ve stated before, the SAT is standardized, and what that often means is that the types of questions they ask and the type of information they expect you to know reappears over and over from test to test. Today’s question of the day, which a surprisingly small percentage of people got correct, is a great example of how the SAT loves to present Right Triangles. So before we send you off to the College Board’s site to give this question “the old college try,” let’s explore what you need to know about right triangles on the SAT.
Many of us remember the Pythagorean Theorem from geometry and might think that’s a good way to solve this question. However, that’s actually not the case on the SAT, since the vast majority of right triangle questions on the SAT are simply variations of 4 Special Right Triangles. If you learn these special right triangles and actively look for them on the SAT, you’ll save yourself a ton of time and effort. If you don’t see any of the special right triangles, then you can always dust off your Pythagorean Theorem.
Special Right Triangles
Whenever you come across a right triangle on the SAT, look for one of the following special right triangles, or a similar triangle with the same ratio of sides.
The four right triangles that hold a special place in ETS’s heart are as follows:
3 – 4 – 5
5 – 12 – 13
30 – 60 – 90
45 – 45- 90
What’s even neater is that at the front of every math section the SAT gives you a formula box that has the ratio of sides for the 45 – 45 – 90 and 30 – 60 – 90 triangles. For example, if you see a right triangle with sides 12 and 9 and hypotenuse x, you should recognize it as a 3 – 4 – 5 triangle where the hypotenuse is 15 (which is 5 x 3), since the sides are 12 (which is 4 x 3) and 9 (3 x 3).
So for the question at hand we have to recognize that it’s a special right triangle, know what the word “congruent” means, and then be careful to apply what we find out about this triangle to the triangle DEF, which they made a little harder to remember because they asked us about something NOT SHOWN (if you missed that point you should check out this post on the single most important SAT technique: RTFQ).
Congruent is the math term that mean they are the same size and shape.
How much do right triangles matter?
On the every SAT there are 54 math questions. On the October 2012 SAT, of those 54 questions, 8 involved a triangle in some way. Of the 8 triangle questions, 4 were right triangles. All four of those right triangle questions were one of the four special right triangles.
Now click on the picture and take a stab at answering the question. If you have trouble, please post your questions in the comments below and we’ll get back to you! Good luck!