{"id":6733,"date":"2016-05-06T13:40:52","date_gmt":"2016-05-06T20:40:52","guid":{"rendered":"https:\/\/magoosh.com\/act\/?p=6733"},"modified":"2018-10-24T02:43:56","modified_gmt":"2018-10-24T09:43:56","slug":"act-geometry-study-guide","status":"publish","type":"post","link":"https:\/\/magoosh.com\/act\/act-geometry-study-guide\/","title":{"rendered":"ACT Geometry Study Guide"},"content":{"rendered":"

About \u00bc of the ACT math test<\/a> 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.<\/p>\n

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.<\/p>\n

Here’s a checklist of all the stuff you will need to know, so let’s dive right in!<\/p>\n

Coordinate Geometry<\/h2>\n

Number lines and Inequalities<\/strong><\/p>\n

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.<\/p>\n

X and Y-Coordinate Plane<\/strong><\/p>\n

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.<\/p>\n

Distance and Midpoint<\/strong><\/p>\n

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.<\/p>\n

Slope<\/strong><\/p>\n

The slope of two points is \u201crise over run.\u201d 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.<\/p>\n

Parallel and Perpendicular lines<\/strong><\/p>\n

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.<\/p>\n

For example,<\/p>\n

y = (3\/4)x + 5
\ny = -(4\/3)x<\/p>\n

are perpendicular.<\/p>\n

Equation of a Line<\/strong><\/p>\n

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

Graphing Equations<\/strong><\/p>\n

Know the basic shape of a linear, quadratic, and cubic equation. Make sure that you can identify and match a graph to its equation.<\/p>\n

Plane Geometry<\/h2>\n

Angles and Lines<\/strong><\/p>\n

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.<\/p>\n

Triangles<\/strong><\/p>\n

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:<\/p>\n