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!
For triangle XYZ with one base angle of 35 degrees, is XY = YZ?
(1) XZ = 5
(2) One base angle is 35 degrees.
The answer is (D).
Notice how we cannot solve for the side lengths in this triangle because we are only given the value of one side and one angle. We cannot determine the relationship between XY and YZ.
Now that you’ve refreshed on Triangles, try some Geometry questions out in Veritas Prep’s own question bank!
Vivian Kerr is a regular contributor to the Veritas Prep blog, providing tips and tricks to help students better prepare for the GMAT and the SAT.