SAT Geometry: Mastering Triangles

This tip for improving your SAT score was provided by Jake Davidson at Veritas Prep.

Geometry is one of the toughest subconcepts of the SAT math section for students to master. There are

a few reasons for this. Usually, geometry is taught in between Algebra 1 and 2 in school, so it’s not as fresh in the mind as the other two. A lot of geometry in school focuses on proofs and theorems, while the SAT is mostly centered on multiple-choice circle and triangle problems. In general, the questions on the SAT are looking to test students’ ability to problem-solve and think outside the box.

Many of the questions related to geometry appear on the surface to be very difficult, but once you are able to remove a layer or two of misdirection, it becomes simple arithmetic. The key is building up the skills and test-taking awareness to recognize the traps and avoid them so you can answer the questions correctly. A lot of this comes from simply working on a large volume of practice problems and getting familiar with the way questions are worded. There are only five or six types of base questions that you will generally see on the test in regard to geometry.

Having the comfort to work with these problems and the easy pattern recognition will have a significant impact on your test day performance. Here are some of the key aspects of triangles to be cognizant of on the test:

Isosceles triangles. Isosceles triangles are all over the SAT. Whether it’s asking you to find an angle within the triangle, identify the length of a side, or a host of other, more convoluted questions, it’s essential to know the basics of an isosceles. On any isosceles, two angles are equal, and their respective sides are also congruent. This means that any question regarding angle sizes will include a multiplication factor of two on a variable.

Additionally, a lot of isosceles-related questions are accompanied by a warning that the figure is not how it may appear. Make sure you pay close attention to this warning when it comes. Most of the time it’s used deliberately to trick the student into thinking the triangle is equilateral, or that two of the sides that have different measures are actually congruent. This is one of the many tricks to be aware of while answering triangle questions on the SAT. Familiarizing yourself with isosceles triangles and the various types of questions that are asked about them will be incredibly helpful come test day.

45-45-90 triangles. These triangles are also common on the SAT. The basic rule to remember on these is that the sides opposite the 45s are equal and in relation to the side opposite the 90-degree measure are 1x to the 90s square root of 2x. Understanding this relationship and being able to manipulate it and work with it will be very helpful, especially with questions about diagonals that cut through squares. These usually create two 45-45-90 triangles, and understanding the relationships can help find the area or perimeter of the squares.

30-60-90 triangles. Another type that’s more common within rectangles, and sometimes within circles, is the 30-60-90 triangle. The measures here have a constant proportion of 1 for the 30-degree measure, a square root of 3 for the 60-degree measure, and 2 for the 90-degree measure. Similar to the 45-45-90 triangles, these are well-represented among the geometry questions, and it’s imperative to know them inside and out to earn a high score on the math section.

Overall, these are just a few of the various intricacies for geometry on the SAT, but getting these down will ensure success on the bulk of all questions related to triangles, whether they’re standalone or appear within circles and squares. Gaining familiarity with these figures is the best way to excel fully on the toughest part of the math section.

Plan on taking the SAT soon? Take advantage of Veritas Prep’s free SAT resources, including free SAT video lessons.

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