# Triangles

## Geometry: Triangles

Read the following SAT test question and then select the correct answer.

Approach all math questions the same way so that you can be confident in your method.  Start by reading the question carefully and making a note of the bottom line – the answer that you must find.  Then, assess your options and choose the most efficient method to attack the problem.  When you have found an answer, loop back to make sure that it is your bottom line.

In the triangles above, 3(y – x) =

Bottom Line: 3(yx) = ?  (Don’t solve for x or y and think that you are finished!)

Assess your Options:  The wonderful thing about geometry questions is that there is often more than one way to get to an answer.  The tricky thing is that using some geometry rules will take longer than others.  For example, you could use the rule that all degrees in a triangle add up to 180 degrees.  Then you would write out an equation to solve for the missing variables in each triangle.  This is the method used on collegeboard.org.  However, if you have special triangles memorized, you can save a lot of time.

Attack the Problem:  The first triangle is a right isosceles triangle.  You know this because it has one right angle, and the other two angles are equal.  This is a special triangle that is very common, so you should memorize the fact that its angles measure 45, 45, and 90 degrees.  The x is equal to 45.

Now look at the second triangle.  It is an equilateral triangle.  You know this because all three angles are equal.  You should memorize the fact that all the angles in an equilateral triangle equal 60 degrees.  The y is equal to 60.

Now that you know what the x and y are, plug these numbers into your equation.

3(yx) =
3(60 – 45) = 45

Loop Back:  You solved for your bottom line, so you are ready to look at the answer choices.

(A) 15
(B) 30
(C) 45
(D) 60
(E) 105

On sat.collegeboard.org, 77% of the responses were correct.

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