Mastering Triangles on the GRE
Understanding the basic properties of triangles can be an amazing savings of time and frustration on the GRE. Once you’ve mastered triangle properties, you’ll find that many geometry problems become quite simple. But — you must invest the time and energy to internalize the properties!
These are the most common triplets and combinations on the GRE. Instead of having to toil through the Pythagorean triplets to understand the relationships of triangle side lengths, have these memorized. Your ability to simple plug in numbers instead of calculating saves will save you a lot of time and leaves less room for error. These triangles are consistently tested on the GRE.
GRE 3:4:5 triangles
6:8:10 (multiplying all the numbers by 2)
9:12:15 (multiplying all the original numbers by 3)
12:16: 20 (multiplying all the original numbers by 4)
15: 20: 25 (multiplying all the original numbers by 5)
GRE 5:12:13 triangles
10: 24: 26
15: 36: 39
GRE 7: 24:25
14: 48: 50
These are some of the more uncommon Pythagorean triplets that may be used on the GRE. However, you might want to memorize them instead of working out a^2 + b^2 = c^2.
a | b | c |
1 | 0 | 1 |
3 | 4 | 5 |
5 | 12 | 13 |
7 | 24 | 25 |
9 | 40 | 41 |
11 | 60 | 61 |
13 | 84 | 85 |
15 | 112 | 113 |
17 | 144 | 145 |
19 | 180 | 181 |
21 | 220 | 221 |
23 | 264 | 265 |
GRE Specialty right triangles
45 degrees 45 degrees 90 degrees
X X X radical 2
30 degrees 60 degrees 90 degrees
X X radical 3 2X
There is a lot of stuff that needs to be memorized here, but it is well worth it. It will translate directly into points on Test Day! Practicing triangle problems will help many of us commit these formulas to memory. Being able to see the connection between the different shapes makes memorizing much easier!