About This Chapter
AFOQT: Circles & Triangles - Chapter Summary
Use the lessons in this chapter to develop a deeper understanding of triangles and circles before you take the AFOQT test. Completing this chapter prepares you to answer questions regarding:
- Area and circumference of circles
- Central and inscribed angles
- Measure of an arc
- Tangent of circles and measurements using tagents
- Properties and classification of triangles
- Triangle angles
- Triangle congruence postulates
- The AAS, HA, HL and Pythagorean theorems
Learning new details or reviewing topics you already know about circles and triangles is made simple thanks to the video and text lessons in this chapter. Each video is taught by a professional instructor, and you can use the self-assessment quizzes to gauge your knowledge and skills to see if you are ready for the real exam.
1. 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.
2. Central and Inscribed Angles: Definitions and Examples
When we're working with circles, there are two key angles to know: central angles and inscribed angles. These angles have a few special theorems, which we'll discuss and practice using in this lesson.
3. Measure of an Arc: Process & Practice
What is the measure of an arc? And what is the difference between a minor arc and a major arc? Find out all that and practice finding the measure of an arc in this lesson.
4. Tangent of a Circle: Definition & Theorems
What happens when a line just barely touches a circle? It's a tangent! In this lesson, we'll learn all about tangents to circles, including a few key theorems. We'll also look at tangent circles.
5. Measurements of Angles Involving Tangents, Chords & Secants
When lines and circles meet, angles are formed. Fortunately, we can determine the measure of these angles, whether they're formed by tangents, secants or chords, just by knowing the measure of the created arcs.
6. Measurements of Lengths Involving Tangents, Chords and Secants
The lengths of chords, tangents and secants take on unique relationships when they're drawn on circles. In this lesson, we'll define those relationships and see them in action.
7. 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.
8. Classifying Triangles by Angles and Sides
Not all triangles are the same. There are equilateral, isosceles and scalene triangles. Then there are right, acute and obtuse triangles. In this lesson, we'll learn how to classify triangles using their sides and angles.
9. Interior and Exterior Angles of Triangles: Definition & Examples
Knowing just a few things about the interior or exterior angles of triangles is sometimes all you need to put all the pieces together. Find out more in this lesson.
10. 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.
11. Triangle Congruence Postulates: SAS, ASA & SSS
When we have two triangles, how can we tell if they're congruent? They may look the same, but you can be certain by using one of several triangle congruence postulates, such as SSS, SAS or ASA.
12. The AAS (Angle-Angle-Side) Theorem: Proof and Examples
When trying to find out if triangles are congruent, it's helpful to have as many tools as possible. In this lesson, we'll add to our congruence toolbox by learning about the AAS theorem, or angle-angle-side.
13. The HA (Hypotenuse Angle) Theorem: Proof, Explanation, & Examples
In this lesson, we'll learn about the hypotenuse angle theorem. With this theorem, we can prove two right triangles are congruent with just congruent hypotenuses and acute angles.
14. The HL (Hypotenuse Leg) Theorem: Definition, Proof, & Examples
In this lesson, we'll learn about the hypotenuse leg theorem. This theorem enables us to prove two right triangles are congruent based on just two sides.
15. Pythagorean Theorem: Definition & Example
Learn what the Pythagorean Theorem says about a right triangle and the relationships of its three sides to each other by watching this video lesson. Also learn how you can use this to your advantage when solving problems.
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Other chapters within the AFOQT: Practice & Study Guide course
- AFOQT: Word Comprehension
- AFOQT: Analogies
- AFOQT: Arithmetic Comprehension
- AFOQT: Arithmetic Equations
- AFOQT: Factoring
- AFOQT: Exponents & Roots
- AFOQT: Word Problems
- AFOQT: Algebraic Expressions
- AFOQT: Graphs, Linear Equations & Parabolas
- AFOQT: Quadratic Equations
- AFOQT: Polynomials, Functions & Rational Expressions
- AFOQT: Principles of Geometry
- AFOQT: Lines & Angles
- AFOQT: Rectangles & Solids
- AFOQT: Figures & Polygons
- AFOQT: Three-dimensional Blocks
- AFOQT: Object Visualization & Manipulation
- AFOQT: Table Knowledge
- AFOQT: Instrument Knowledge
- AFOQT: Aviation
- AFOQT: The Metric System & Scientific Notation
- AFOQT: Atoms & Matter
- AFOQT: Thermodynamics & Electricity
- AFOQT: Magnetism
- AFOQT: Earth Science
- AFOQT: Biomolecules & Cells
- AFOQT: Human Anatomy
- AFOQT: Personality Traits & Attitudes
- AFOQT Flashcards