# Ch 32: 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.

### 1. How to Solve Visualizing Geometry Problems

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.

### 2. Types of Angles: Vertical, Corresponding, Alternate Interior & Others

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.

### 3. Parallel, Perpendicular and Transverse Lines

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.

### 4. Properties of Shapes: Rectangles, Squares and Rhombuses

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.

### 5. Parallelograms: Definition, Properties, and Proof Theorems

Watch this video lesson to learn how you can identify parallelograms. You will see the unique properties that belong to the parallelogram. You will see the special side and angle characteristics needed to prove a certain shape is a parallelogram.

### 6. Trapezoids: Definition and Properties

Watch this video lesson to learn what a trapezoid has to do with a triangle. Also, learn the special words that describe the various parts of a trapezoid. You will also see special types of trapezoids.

### 7. Circles: Area and Circumference

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.

### 8. Properties of Shapes: Circles

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.

### 9. How to Calculate the Volumes of Basic Shapes

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?

### 10. Planes and the Polyhedron: Definition and Example

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.

### 11. Prisms: Definition, Area & Volume

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.

### 12. Pyramids: Definition, Area & 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.

### 13. What Are Cylinders? - Definition, Area & 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.

### 14. Cones: Definition, Area & Volume

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.

### 15. Spheres: Definition, Area & Volume

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.

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### Other Chapters

Other chapters within the ACT Prep: Practice & Study Guide course

- ACT: About the Test
- ACT English: Section Overview
- ACT English: Punctuation
- ACT English: Grammar and Usage
- ACT English: Sentence Structure
- ACT English: Parts of an Essay
- ACT English: Rhetorical Strategy
- ACT English: Organization
- ACT English: Style
- ACT Math: Overview
- ACT Math: Number & Quantity
- ACT Math: Pre-Algebra
- ACT Math: Algebraic Expressions
- ACT Math: Radicals
- ACT Math: Linear Equations
- ACT Math: Functions
- ACT Math: Types of Functions
- ACT Math: Absolute Value
- ACT Math: Matrices
- ACT Math: Inequalities
- ACT Math: Probability, Combinations & Factorial
- ACT Math: Data and Statistics
- ACT Math: Exponents
- ACT Math: Polynomials and Quadratics
- ACT Math: Rational Equations and Expressions
- ACT Math: Sequences
- ACT Math: Complex Numbers
- ACT Math: Exponentials and Logarithms
- ACT Math: Coordinate Geometry
- ACT Math: Conic Sections
- ACT Math: Triangles
- ACT Math: Lines and Angles
- ACT Math: Trigonometry
- ACT Science Reasoning: Overview
- ACT Science Reasoning: Fundamentals of Science
- ACT Science Reasoning: Evaluating Models
- ACT Reading: Overview
- ACT Reading: Question Types
- ACT Reading: Understanding Reading Passages
- ACT Reading: Word Meanings and Choice
- ACT Reading: Analyzing Reading Passages
- ACT Reading: Practice
- ACT Writing: Overview
- ACT Writing: Essay Skills
- ACT Writing: Planning and Writing
- ACT Writing: Advanced Writing Skills
- ACT Prep Flashcards