About This Chapter
ILTS Mathematics: Points, Lines, Planes & Space - Chapter Summary
Preparing for professional licensure can cause panic and stress, but if you use our chapter to review the major keywords and formulas associated with points, lines, planes, and space, you may feel more confident about this topic, which means you should have a calmer mind when you sit for the ILTS Mathematics Test. Our easy-to-follow video lessons give you a useful recap of all the key concepts covered on the test, such as the following:
- Geometry's undefined terms
- Euclid's axiomatic geometry
- The format and purpose of geometric proofs
- The functions of an indirect proof
- Using angles and lines to make geometric constructions
- The midpoint theorem and line segment bisection
- Splitting line segments into equal sections
- An analysis of non-Euclidean and Euclidean geometry
As you go through memorization drills for the ILTS Mathematics Test, our video lessons can help give you a more visual reminder about how to use proofs to solve geometric equations. The key terms and formulas are bolded in our transcripts, so you can quickly identify the midpoint theorem and other theories. Since you are getting ready for the test that will make the difference between you having or not having a teaching position in Illinois, remember that every study guide, video, and assessment tool we offer can be accessed around the clock on any Wi-Fi device. In other words, whether you're on a regular study schedule or working late-night cram sessions, we have your back.
1. Undefined Terms of Geometry: Concepts & Significance
What do points, lines, planes, and sets have in common? Watch this video lesson to find out what they are, what they look like, and why they are called undefined terms.
2. Euclid's Axiomatic Geometry: Developments & Postulates
Learn how the way we do proofs in geometry had its start with Euclid in this video lesson. Learn about his contributions to the geometry we know today. Also learn about the five basic truths that he used as a basis for all other teachings.
3. Geometric Proofs: Definition and Format
Do you have something to prove? Can you explain why? In this lesson, we'll learn all about geometric proofs, including the parts that comprise a proof.
4. Indirect Proof in Geometry: Definition & Examples
There are many different methods that can be used to prove a given theory. One of those methods is indirect proof. In this lesson, we will explore indirect proof and learn the steps taken to use this method to prove a given theory.
5. Geometric Constructions Using Lines and Angles
Watch this video lesson to learn about geometric construction and how you can copy line segments and angles without using any numbers. All you need is a straight edge and a compass.
6. Line Segment Bisection & Midpoint Theorem: Geometric Construction
Watch this video lesson and you will learn how to bisect a line segment without measurements using just a compass and a straight edge. You'll also learn about the midpoint theorem, which lets you calculate the midpoint if you have the measurements.
7. Dividing Line Segments into Equal Parts: Geometric Construction
Watch this video lesson to learn one way to easily divide any line segment into as many equal parts as you need. Also, learn where in real life this skill comes in handy.
8. Differences Between Euclidean & Non-Euclidean Geometry
Euclidean geometry is the study of the geometry of flat surfaces, while non-Euclidean geometries deal with curved surfaces. Here, we'll learn about the differences between these mathematical systems and the different types of non-Euclidean geometry.
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Other chapters within the ILTS Mathematics (208): Test Practice and Study Guide course
- ILTS Mathematics: Concepts & Skills
- ILTS Mathematics: Logic & Reasoning
- ILTS Mathematics: Using Technology for Math
- ILTS Mathematics: Number Theory
- ILTS Mathematics: Solving Number Problems
- ILTS Mathematics: Real & Complex Numbers
- ILTS Mathematics: Measurement
- ILTS Mathematics: Multidimensional Objects
- ILTS Mathematics: Variables & Patterns
- ILTS Mathematics: Linear Relations & Functions
- ILTS Mathematics: Quadratic Relations & Functions
- ILTS Mathematics: Absolute Value
- ILTS Mathematics: Polynomials
- ILTS Mathematics: Radical Functions
- ILTS Mathematics: Rational Functions
- ILTS Mathematics: Exponential Functions
- ILTS Mathematics: Logarithmic Functions
- ILTS Mathematics: Trigonometric Functions
- ILTS Mathematics: Calculus
- ILTS Mathematics: 2D & 3D Shapes
- ILTS Mathematics: Spatial Visualization
- ILTS Mathematics: Congruence, Similarity & Symmetry
- ILTS Mathematics: Probability Theory & Techniques
- ILTS Mathematics: Collecting & Representing Data
- ILTS Mathematics: Using Data to Make Predictions
- ILTS Mathematics Flashcards