Equilateral Triangles
An equilateral triangle has three equal sides and three congruent 60º angles.
Based on the proportionality rule, if a triangle has three equal sides, that triangle must also have three equal angles. Similarly, if you know that a triangle has three equal angles, then you know it also has three equal sides.
Right Triangles
A triangle that contains a right angle is called a right triangle. The side opposite the right angle is called the hypotenuse. The other two sides are called legs. The angles opposite the legs of a right triangle are complementary (they add up to 90º).
In the figure above, 
is the right angle (as indicated by the box drawn in the angle), side c is the hypotenuse, and sides a and b are the legs.
If triangles are an SAT favorite, then right triangles are SAT darlings. In other words, know these rules. And know the Pythagorean theorem.
The Pythagorean Theorem
The Greeks spent a lot of time reading, eating grapes, and riding around on donkeys. They also enjoyed the occasional mathematical epiphany. One day, Pythagoras discovered that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. “Eureka!” he said, and the SAT had a new topic to test.
Here’s the Pythagorean theorem: In a right triangle, a2 + b2 = c2:
where c is the length of the hypotenuse and a and b are the lengths of the two legs.
The Pythagorean theorem means that if you know the measures of two sides of a right triangle, you can always find the third. “Eureka!” you say.
Pythagorean Triples
Because right triangles obey the Pythagorean theorem, only a specific few have side lengths that are all integers. For example, a right triangle with legs of length 3 and 5 has a hypotenuse of length 
= 5.83.
The few sets of three integers that do obey the Pythagorean theorem and can therefore be the lengths of the sides of a right triangle are called Pythagorean triples. Here are some common ones:
{3, 4, 5}
{5, 12, 13}
{7, 24, 25}
{8, 15, 17}
In addition to these Pythagorean triples, you should also watch out for their multiples. For example, {6, 8, 10} is a Pythagorean triple, since it is a multiple of {3, 4, 5}.
The SAT is full of right triangles whose side lengths are Pythagorean triples. Study the ones above and their multiples. Identifying Pythagorean triples will help you cut the amount of time you spend doing calculations. In fact, you may not have to do any calculations if you get these down cold.
Extra-Special Right Triangles
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