# Triangles

History.com's This Day in History is a great place to look for interesting historical events that might otherwise be overlooked. Common examples like Martin Luther King Jr. or the Holocaust will not make your essay stand out, but the fact that on May 9th, 1950, L. Ron Hubbard published Dianetics or that in 2001, soccer fans were trampled in Ghana will make your essay stronger.

## 5/9 Geometry: Triangles

Remember to always follow the Knowsys Method for math problems. The method will save you time and errors not only on the SAT but also in your regular math classes and problems. First, read the question carefully and identify the bottom line. Once you know what the problem is asking, assess your options by asking "What could I do?" "What should I do?" Select the most efficient method, attack the problem, and loop back to make sure that you answered the question correctly.

If triangle ABC above is congruent to triangle DEF (not shown), which of the following must be the length of one side of triangle DEF?

First, at the top of your scratch work, write one side of DEF = ?

Next, assess your options. How can you find the side lengths of a triangle that is not shown? The problem mentions that ABC and DEF are congruent, which means all their side lengths and angle measurements are the same. That means that you can simply change the labels on ABC to DEF. To find the answer, though, you will need to figure out the side lengths. You could try to use the Pythagorean Theorem here, but it would be very difficult. Instead, you should notice that the triangle is one of the special right triangles that you have memorized. You can use that information to find the side lengths.

Triangle DEF is a 30-60-90, which means the side lengths are $x-x\sqrt{3}-2x$. The hypotenuse is 12, so 12 = 2s and 6 = s. The hypotenuse of the triangle is 12, the short leg is 6, and the other leg is $6\sqrt{3}$.

Loop back to the bottom line. You are looking for any side of Triangle DEF, so now that you have all three, you only need to look at the answer choices and find one that matches any of these three numbers.

A) 18

B) 24

C) $3\sqrt{6}$

D) $6\sqrt{3}$

E) It cannot be determined from the information given.