# ACT Geometry Study Guide

About ¼ of the ACT math test will revolve around geometry problems. That’s quite a hefty portion of the test, so be prepared to know your shapes, lines, and graphs well in order to get a good overall math score.

Although you won’t be expected to dive deeply into any particular sub-topic within geometry, you at least need to know and memorize the basic formulas and equations that you would learn in pre-algebra, algebra I, and high school geometry.

Here’s a checklist of all the stuff you will need to know, so let’s dive right in!

## Coordinate Geometry

Number lines and Inequalities

This involves knowing how to represent inequalities using a number line. You may be asked to figure out which direction the arrow is supposed to point (and if there should even be one). Pay attention to whether there is a line underneath the greater than or less than sign.

X and Y-Coordinate Plane

Remember that the x-axis is on the horizontal line and the y-axis is on the vertical line. There are four quadrants, starting with the upper right and going counterclockwise to the lower right.

Distance and Midpoint

You will need to know how to find the distance and midpoint between two points. The midpoint formula is simple enough, but if you ever forget the distance formula, remember that you are just using the Pythagorean Theorem to find the hypotenuse.

Slope

The slope of two points is “rise over run.” The slope of a line is m where y = mx + b. The b represents the y-intercept, or where the line crosses the y-axis. You can draw in this line by connecting two points together if you are only given two points and no equation to work with.

Parallel and Perpendicular lines

Parallel lines have the same slope, but they don’t have the same y-intercept. Perpendicular lines are a bit more complicated. Perpendicular slopes are negative reciprocals of each other.

For example,

y = (3/4)x + 5
y = -(4/3)x

are perpendicular.

Equation of a Line

The easiest way to graph the equation of a line is by first turning the equation into slope-intercept form, or y = mx + b.

Graphing Equations

Know the basic shape of a linear, quadratic, and cubic equation. Make sure that you can identify and match a graph to its equation.

## Plane Geometry

Angles and Lines

Know the vocabulary for the different types of angles (right, acute, obtuse, vertical, supplementary, complementary) and lines (ray, line segment, line). Make sure you know how transversals work as well.

Triangles

There are many different properties of triangles that you will need to know. As far as basic shapes, you will be tested the most on this particular shape, so it will pay dividends to know this sub-topic inside and out:

• sum of three angles in a triangle
• the relationship between interior and exterior angles
• the relationship between the angles to the sides
• Pythagorean Theorem
• area and perimeter of a triangle
• each side length is smaller than the other two side lengths added together
• isosceles, equilateral, and right triangles
• special right triangles
• similarity in triangles

## Other Shapes

These don’t come up quite as often, but you will see these from time to time. Prepare for them now so that they don’t take you by surprise on the test:

• area and perimeter of a square, circle, rectangle, parallelogram, and trapezoid
• basic properties of a square, circle, rectangle, parallelogram, and trapezoid
• diagonal length of a rectangular prism or cube

## Some Final Tips

Unlike algebra, geometry is more picture-oriented and less about doing calculations and crunching numbers. You’ll need to get used to seeing, interpreting, and diagrams and shapes.

More importantly, you have to develop the skills to take geometry word problems and picture what the ACT test makers are trying to describe. If you focus on analyzing the patterns in the wording of ACT math problems, you’ll be able to get faster at figuring out what the problem is asking for.

## Author

• Minh's passion for helping students succeed grew during his time as a career counselor at the University of California, Irvine. Now, he's helping students all over the world by spilling SAT/ACT secrets through blog posts on Magoosh. When he's not busy tutoring or writing, he enjoys playing guitar, traveling, and talking about himself in third-person.