ACT Geometry Equations Practice

Geometry in Mathematics

Overview

Geometry is a branch of mathematics concerned with the properties and measurements of points, lines, angles, and closed planes, surfaces, and solids. It plays a crucial role in the ACT math section, making up nearly a third of the entire math portion of the test. Understanding the fundamental principles and equations associated with geometry can significantly improve your performance in the test.

Key Equations

The ACT math section features many questions on geometry. To excel in these sections, it's essential to be familiar with the following equations and concepts:

30-60-90 Triangle

When you know that the interior angles of a triangle measure 30 degrees, 60 degrees, and 90 degrees, you can use the equation below to determine the different side lengths.

a² + b² = c²

45-45-90 Triangle

When you know that the interior angles of a triangle measure 45 degrees, 45 degrees, and 90 degrees, you can use the equation below to determine the different side lengths.

a² = b² + c² / 2

Area of Standard Shapes

Square/Rectangle

Area = Base × Height

Triangle

Area = 1/2 (Base × Height)

Circle

Area = π × Radius²

These equations play a central role in solving geometry problems on the ACT. Additionally, you may encounter questions involving solid geometry, which involves three-dimensional shapes like cones, spheres, and cylinders.

Preparation

To prepare for geometry questions on the ACT, it's recommended to focus on the information that you know will show up frequently on the test. Review the equations mentioned earlier and practice solving problems using these equations. Actively engage in quizzing yourself to build confidence and familiarity with the material. Remember, geometry is a big part of the ACT math section, and success relies primarily on your ability to recall and apply the necessary equations correctly.