About This Chapter
Geometry - Chapter Summary
Geometry can seem intimidating, especially since you're dealing with the properties of so many different shapes and figures. We'll make geometry feel easy as pie (or pi) by walking you through the elements of different geometrical figures and showing you how to use those elements to solve math problems. Prior to taking the ASVAB exam, explore the world of points, lines, angles, and two- and three-dimensional shapes until you achieve a greater understanding of basic geometry. These lessons cover:
- Different types of angles
- Perimeters and areas
- Properties of different triangles
- Similar triangles
- The Pythagorean theorem
- Surface-areas and volumes
- Perpendicular and parallel lines
- Pyramids, cones, spheres, rhombuses and cylinders
Our video lessons, developed by a team of awesome instructors, are a great way to learn everything you'll need to know before test day. Use our video transcripts to go over what you've learned and then check out the self-assessments to get a feel for the types of questions you may encounter on the ASVAB.
ASVAB Math Objectives
The Armed Services Vocational Aptitude Battery (ASVAB) is a multiple-choice exam used to test aptitude in certain areas for applicants to the U.S. military. A paper-based Mathematics Knowledge subtest of the ASVAB is comprised of 25 questions, many of which will test your knowledge of geometry, that you will have 24 minutes to complete. There is also computerized version of the test. It has 16 questions that must be answered in 20 minutes. The questions in this subtest account for just over 11% of the exam. Objectives for this chapter include:
- Defining different types of angles and lines
- Identifying two-dimensional shapes and demonstrating how to calculate their perimeters and areas
- Knowing how to use the Pythagorean theorem to work with triangles
- Calculating the surface areas and volumes of different three-dimensional shapes
Getting a handle on geometry with our effortless video lessons will help you greatly in the math section of the ASVAB exam. By the time you're done with our study guide, you'll be ready to take on any geometry questions on the test.
1. Points, Lines & Angles in Geometry
After watching this video lesson, you should understand the basic terms that form the foundation of geometry. Learn what a point is, what a line is, what an angle is, and learn about a special type of angle called a right angle.
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. Overview of the Basic Shapes in Geometry
Watch this video lesson to learn about some basic shapes in geometry. These are the shapes that you will come across most often in math. Watch as triangles, rectangles, pentagons, and circles come by.
5. 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.
6. Triangles: Definition and Properties
What makes a shape a triangle? In this lesson, we'll explore the definition of a triangle, then analyze the parts of triangles, including the vertices, base and height.
7. Perimeter of Triangles and Rectangles
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.
8. Area of Triangles and Rectangles
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.
9. The Pythagorean Theorem: Practice and Application
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.
10. How to Identify Similar Triangles
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.
11. Applications of Similar Triangles
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.
12. Angles and Triangles: Practice Problems
Want more practice solving with angle pairs? How about more review for solving angles in triangles? Look no further. Get more practice here, and test your ability with a quiz.
13. Vertical Angles & Complementary Angles: Definition & Examples
Special angles make your life easier. Learn how you can use the properties of special angles to help you find the measurements of missing angles in this video lesson.
14. Overview of Three-dimensional Shapes in Geometry
We are surrounded by three-dimensional shapes. Watch this video lesson to see what some three-dimensional shapes look like, such as a cube, a sphere, a brick, and a cylinder.
15. How to Find Surface Area of a Cube and a Rectangular Prism
After watching this video lesson, you will be able to use the formula for the surface area of a rectangular prism. You will know what measurements you need to use it and how you can apply it to a cube as well.
16. How to Find Surface Area of a Cylinder
Watch this video lesson to learn the formula you can use to find the surface area of a cylinder. Learn the measurements that you'll need as well as how to use them.
17. How to Find Surface Area of a Pyramid
In this video lesson, we will learn how to take any pyramid, whether it's a pyramid in Egypt or a little toy pyramid, and calculate how much paint we will need to paint it. Learn the formula and what is behind it.
18. Volume of Prisms and Pyramids
In this lesson, we'll learn about prisms and pyramids. We'll look at the different types of prisms and pyramids, as well as practice calculating volume for each shape.
19. Volume of Cylinders, Cones, and Spheres
In this lesson, we'll learn about the volume formulas for cylinders, cones and spheres. We'll also practice using the formula in a variety of real-world examples where knowing how to calculate volume is helpful.
20. Combined Figures: Perimeter, Area, and Volume
Watch this video lesson to learn how you can break up the shapes in a combined figure to easily find the perimeter, area, and volume of the whole figure.
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Other chapters within the ASVAB Mathematics Knowledge: Study Guide & Test Prep course
- ASVAB Math: Basic Arithmetic
- ASVAB Math: Math Expressions and Formulas
- ASVAB Math: Solving Math Word Problems
- ASVAB Math: Rounding Numbers and Decimals
- ASVAB Math: Fractions
- ASVAB Math: Factorials in Math
- ASVAB Math: Reciprocals
- ASVAB Math: Types of Numbers
- ASVAB Math: Patterns & Sequences
- ASVAB Math: Exponents
- ASVAB Math: Properties of Exponents
- ASVAB Math: Algebraic Expressions and Equations
- ASVAB Math: Factoring
- ASVAB Math: Quadratic Equations
- ASVAB Math: Working with Quadratic Equations
- ASVAB Math: Inequalities
- ASVAB Math: Calculating Interest
- ASVAB Math: Circles
- About the ASVAB Test
- ASVAB Mathematics Knowledge Flashcards