In the previous post in this series, we looked at arc measure and arc length. Now it’s time to look at circles and straight lines. What happens when a straight line comes near a circle? In how many ways can these two objects intersect? It turns out, there are three possibilities — see below: no […]

# Archive | GMAT Geometry

Master GMAT geometry with the help of Magoosh’s experts: everything from GMAT geometry questions to what you need for a GMAT geometry cheat sheet.

In the first post in these series, I discussed the basic circle facts. This post concerns angles and circles, and dividing circles by angle. Angles of a Circle Suppose you stand at the center of a circle and turn around that you face each and every point on the circle. You would turn all […]

Sometimes, the best choice from among two options is neither of them! Approaches to the GMAT Quantitative Section Many quantitative problems contain numbers and demand numerical calculations. Others contain variables, and one can use either an algebraic approach or a numeric approach. See this blog post for more on that choice. Folks are often […]

Understand the properties of the GMAT Quantitative section’s two favorite triangles! The two special triangles are right triangles with special angles and side. Like all right triangles, they satisfy the Pythagorean Theorem. These two triangles are “special” because, with just a couple pieces of information, we can figure out all their properties. The GMAT-writers love this […]

The 45º angle Fact: All lines with slopes of 1 make 45º angles with both the x- and y-axes. Conversely, if a line makes a 45º angles with either the x- of y-axes, you know immediately its slope must be . This first fact is true, not only for y = x and y = […]

Using the information given in diagrams to your advantage The following sentences appear in the directions to the GMAT Problem Solving questions. A figure accompanying a problem solving questions is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Many GMAT-takers underestimate […]

Often, when we talk about triangles in the context of the GMAT, we focus on right triangles (a relatively elite category) or the special right triangles (viz. 30-60-90 and 45-45-90 triangles, a hyper-elite category). Elsewhere I have written of that most glorious theorem, the Pythagorean Theorem, which applies to all right triangles. But just as […]

The GMAT quantitative section asks, among other things, about geometry. One of the GMAT’s favorite figures is the isosceles triangle. An isosceles triangle is one that has two congruent sides. Knowing simply that about a triangle has profound implications for answer GMAT Problem Solving & Data Sufficiency questions. Euclid’s Remarkable Theorem Euclid first proved […]

Consider the following geometry Data-Sufficiency Questions. All are related to the diagram below: 1) Is quadrilateral ABCD a square? (1) AB = CD (2) A = 90º (A) Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked. (B) Statement 2 alone is sufficient but statement 1 […]

The GMAT will ask you about geometric solids. The OG tells you that you should expect questions about rectangular solids and cylinders. Here, I will discuss four less common solids that are much less likely to appear on the GMAT Math section: the prism, the pyramid, the cone, and the sphere. For all of these, […]

According to the GMAT OG, there are two 3D solids you should understand in detail are (a) rectangular solids, and (b) cylinders. On any given GMAT, you will see no more than a couple questions on 3D solids, but they definitely could appear, especially if you are already getting many questions right and are moving […]

A Case Study of the Area of an Equilateral Triangle Fact: on the GMAT Math section, you are likely to find questions about the area of an equilateral triangle, and it would be efficient if you knew the formula. (BTW, the formula appears a little further below.) Don’t Merely Memorize I am going to […]

As you may remember from high school, , where b is the base and h is the height. If you are having trouble remembering this, simply remember that a rectangle has an area of , and that a triangle is half a rectangle. Practice Question: Using the Area Formula 1) The figure on […]

There’s a reason this is the most famous theorem in mathematics! This remarkable theorem is one of the most versatile and highly adaptable formulas in existence. Of course, I’m sure you remember that it says: For any right triangle, Of course, if any question […]