# Master the Geometry Section of the GMAT

Need better scores on GMAT Geometry questions? The GMAT loves triangles (no offense, circles). With a clear set of rules and formulas which govern their construction, they are lean, mean, Plane Geometry-machines. Get ANY question with a triangle right as long as you know its foundational properties. Let’s review!

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 Pythagorean Theorem states that a2 + b2 = c2 where a and b are the two shorter sides and c is always the longest side (the side across from the 90 degree angle) of a right triangle. The longest side in a right triangle is called the hypotenuse.

Save valuable time on the GMAT 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, the 13 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 is 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!

Let’s look at a GMAT Data Sufficiency question involving triangles:

For triangle XYZ with one base angle of 35 degrees, is XY = YZ?

(1) XZ = 5

(2) One base angle is 35 degrees.