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This tip on improving your SAT score was provided by Vivian Kerr at Veritas Prep.
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Triangles often appear on the SAT, and there are some basic properties you’ll need to know to rock the SAT math section. A triangle is a three-sided figure. The sum of the interior angles is always 180 degrees. To find the area of a triangle, we use the formula A = ½ bh, where b = base and h = height. The base and the height of the triangle must always form a 90-degree angle. Keep in mind that the height can be inside or outside the triangle.

The Triangle Inequality Theorem states that for any side of a triangle, its value must be between the sum and the difference of the other two sides (non-inclusive). For example, if we have a triangle with two sides, 3 and 9, can 6 be the value of the third side? Let’s consider: We know the sum of 3 + 9 is 12, and the difference of 9- 3 is 6, so the third side must be *between* 6 and 12. Since 6 is not between those two numbers, then 6 cannot be the value of the third side.

The Pythagorean Theorem states that a^{2} + b^{2} = c^{2} where a and b are the two shorter sides and c is always the longest side or the hypotenuse (the side across from the 90-degree angle) of a right triangle. In this triangle, the “?” side is the hypotenuse. Let’s plug the values for the other two sides into the Pythagorean Theorem to solve:

a^{2} + b^{2} = c^{2}

8^{2} + 5^{2} = c^{2} 64 + 25 = c^{2} 89 = c^{2}

To remove the exponent (^{2}), we must take the square root (√) of both sides.

√89 = c

Save valuable time on the SAT by memorizing the common Pythagorean triplets. You often encounter right triangles with the ratios of 3:4:5 and 5:12:13. These ratios will also be true for any multiples of 3:4:5 and 5:12:13 such as 6:8:10 or 10:24:26. For example, in this triangle we know the third side must be 5, even without using the Pythagorean Theorem, because we know 5:12:13 is a common triplet.

Be cautious, however, because the 13, or longest side/hypotenuse, must always be across from the 90-degree angle.

There are two special right triangles. The first is a 30-60-90 triangle. Its sides will always be in a ratio of x: x√3 : 2x. The other special triangle is the 45-45-90 triangle. Its sides will always be in a ratio of x: x: x√2. It’s important to remember that for the 30-60-90 triangle, the hypotenuse is the side that has the ratio of 2x. Don’t confuse it with the 45-45-90 ratio and think that the x√3 should be there.

*For triangle question practice, take a full-length SAT practice test to sharpen your skills. *