# ACT Math: Plane Geometry

## About this chapter

## ACT Math: Plane Geometry - Chapter Summary

Go over these crucial plane geometry concepts for help in passing the math section of the ACT test. Our short video lessons address the following topics:

- Types of angles
- Types of lines
- Properties of circles, rectangles, triangles and special right triangles
- Perimeter and area of triangles and rectangles
- Pythagorean theorem
- Area and circumference of circles
- Volumes of basic shapes

This chapter includes review in the practice and application of finding distance with the Pythagorean theorem. Go over vertical, corresponding and alternate interior angles in addition to parallel, perpendicular and transverse lines. Take the quizzes for immediate feedback, to see if you're ready for the ACT math test.

### ACT Math Objectives

The math portion of the ACT test is a 60-question, 60-minute assessment. The multiple-choice questions check your reasoning skills in the solutions of math problems. The math test addresses the following six areas:

- Plane geometry
- Coordinate geometry
- Trigonometry
- Pre-algebra
- Elementary algebra
- Intermediate algebra

The plane geometry portion of the test comprises 23% of the problems. Questions check your understanding of the following:

- Properties and relations of plane figures
- Relations among parallel and perpendicular lines
- Properties of trapezoids, parallelograms, rectangles, triangles and circles
- Transformations
- Proof techniques
- Volume
- Geometry applications to three dimensions

You'll receive four scores for the math test, including three sub-scores in plane geometry/trigonometry, pre-algebra/elementary algebra and intermediate algebra/coordinate geometry, in addition to an overall score for all 60 questions.

A picture is worth a thousand words, but sometimes drawing that picture can be like doing origami with your eyes closed. Practice translating complex problems into simple, meaningful images in this lesson.

In addition to basic right, acute, or obtuse angles, there are many other types of angles or angle relationships. In this lesson, we will learn to identify these angle relationships and discuss their measurements.

What are the different types of lines? Where are they visible in the real world and how can you recognize them? Find out here and test your knowledge with a quiz.

What's the difference between a square and a rectangle? What about a rhombus and a square? In this lesson, we'll look at the properties of these shapes.

Isosceles, equilateral and obtuse, oh my! These are terms for triangles. But what do they mean? In this lesson, we'll explore the properties of triangles and take a closer look at the different types of triangles you may encounter.

Without realizing it, we calculate and use the perimeter of triangles and rectangles in regular everyday situations. Learn more about the perimeter of triangles and rectangles in this lesson, and test your knowledge with a quiz.

How do you find out the area of rectangles and triangles? Learn how in this lesson! We'll look at the formulas, then practice solving problems for each shape.

How much faster is it to cut the corners in a race around the block? In this lesson, review the Pythagorean Theorem, and figure out how to solve without a right triangle.

Similar triangles are used to solve problems in everyday situations. Learn how to solve with similar triangles here, and then test your understanding with a quiz.

Similar triangles have the same characteristics as similar figures but can be identified much more easily. Learn the shortcuts for identifying similar triangles here and test your ability with a quiz.

The Pythagorean theorem is one of the most famous geometric theorems. Written by the Greek mathematician Pythagoras, this theorem makes it possible to find a missing side length of a right triangle. Learn more about the famous theorem here and test your understanding with a quiz.

Not all right triangles are the same. In this lesson, we'll look at two special right triangles (30-60-90 and 45-45-90) that have unique properties to help you quickly and easily solve certain triangle problems.

Are you up to speed on your Pythagorean triples? If you could use a little help with that, watch this lesson to learn what 3-4-5 triangles are, how they're used, and why they're important.

Understanding how to calculate the area and circumference of circles plays a vital role in some of our everyday functions. They serve as the foundation for operating with three-dimensional figures. Learn more about the area and circumference of circles in this lesson.

Circles are fundamental to everything we do. But did you know they're much more than just round shapes? In this lesson, we'll look at the various parts of circles and how they all relate.

Squares pegs = square holes. Triangular pegs = triangular holes. But where does a sphere go? In this lesson, review volumes of common shapes while contrasting a sphere and a cylinder - after all, they both go into the circular hole... right?

Did you ever wonder what the pyramids in Egypt have to do with math? Watch this video to find out where in math a pyramid comes into play. Also, learn how flat, 2-dimensional shapes also come into play.

Watch this video lesson and you will see that there are different kinds of prisms. You will also learn how to separate a prism into its various parts so you can easily find the surface area. You will also learn the formula for the volume.

Do you think of the great pyramids of Egypt when you hear the word pyramids? Watch this video lesson to learn why they are called pyramids and also how to find their surface area and volume.

Watch this video lesson to learn why soda cans are cylinders and the method by which you can discover how much soda can fit inside by finding the volume. You will also learn about finding a cylinder's surface area.

Watch this video lesson to learn where in the real world you will see cones. Also, you will learn the formulas for finding the surface area and volume of these cones.

Watch this video lesson to learn how you can find the surface area and volume of spheres. Learn the formulas and measurements you need to solve problems and discover how to identify spheres in the real world.

**Watched all the videos in this chapter?**