# Ch 22: Michigan Merit Exam - Math: Euclidean & Coordinate Geometry

### About This Chapter

## Michigan Merit Exam - Math: Euclidean & Coordinate Geometry - Chapter Summary

You can watch enjoyable video lessons about ways to create geometric constructions. You will also learn about what makes a line transversal or perpendicular. Short quiz assessments provided at the end of each lesson will test how well you can make figures like a square or an equilateral triangle. This Euclidean & Coordinate Geometry chapter's combination of video lessons and quizzes will help you master the following items for your exam:

- Definition of rays and line segments
- Lines, angles, and points
- Tools and strategies for creating and practicing geometric constructions
- Midpoint theorem and line segment bisection
- Division of line segments
- Line forms: perpendicular, transverse, and parallel
- Creating perpendicular lines
- Kinds of angles
- Definition and creation of an angle bisector
- Creation of squares, equilateral triangles, and regular hexagons
- Euclid's axiomatic geometry
- Geometric terms
- Undefined terms
- Characteristics and postulates of figures

While you are progressing through the video lessons, you can use the timeline to go back to specific parts of them. This way, you do not have to re-watch the videos in their entirety. If you answer any of your quiz questions incorrectly, you can easily view the parts of the videos that address the answers by clicking 'Watch Answers' Let our instructors or experts know if you have any questions.

### Michigan Merit Exam - Math: Euclidean & Coordinate Geometry Objectives

This chapter's resources link to the Geometry & Trigonometry part which is one part of the four-part Michigan Merit Exam's math portion. You will be responsible for answering approximately 25 total multiple-choice math questions on paper. You may also see questions on the exam that ask you about the characteristics and creation of other figures and identification of the elements of Euclidean geometry.

### 1. Line Segments & Rays: Definition & Measurement

Watch this video lesson to learn the difference between a line segment and a ray. You will also learn how to measure and add line segments. Learn why you can't measure or add a ray.

### 2. 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.

### 3. Methods & Tools for Making Geometric Constructions

Did you know that it's possible to do math without using numbers? This is exactly what Euclid did when he showed how to solve mathematical problems by drawing them out instead of with numbers.

### 4. Practice Making Geometric Constructions with Tools

There are a number of tools available to geometry students to help make their work a bit easier. In this lesson, we will review how to use many of them in order for you to get the most out of every geometry class.

### 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. 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.

### 9. Constructing Perpendicular Lines in Geometry

In this video lesson, you will see how to use geometric construction to draw perpendicular lines. Learn why geometric construction is useful. Also find out the only two tools in addition to your pencil that you need to do this.

### 10. 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.

### 11. Constructing an Angle Bisector in Geometry

Watch this video lesson to learn a cool way to split an angle in half. You can use this method to split a pie slice in half where you can be sure each side is equal.

### 12. Constructing Equilateral Triangles, Squares, and Regular Hexagons Inscribed in Circles

Constructing an accurate triangle, square, or hexagon within a circle is a matter of a few simple steps, and can be extremely practical. In this lesson, we'll practice the construction of those three shapes.

### 13. 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.

### 14. 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.

### 15. Properties and Postulates of Geometric Figures

In geometry, there are some basic postulates that are relied upon as the basis for other theorems. Watch this video to learn about the postulates that deal with points, lines, and planes.

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### Other Chapters

Other chapters within the Michigan Merit Exam - Math: Test Prep & Practice course

- Michigan Merit Exam - Math: Number Systems & Number Sense
- Michigan Merit Exam - Math: Representations & Relationships
- Michigan Merit Exam - Math: Counting & Probabilistic Reasoning
- Michigan Merit Exam - Math: Using Real & Complex Numbers
- Michigan Merit Exam - Math: Sequences & Iteration
- Michigan Merit Exam - Math: Measurement Units, Calculations & Scales
- Michigan Merit Exam - Math: Understanding Error
- Michigan Merit Exam - Math: Mathematical Reasoning
- Michigan Merit Exam - Math: Language, Laws & Proof of Logic
- Michigan Merit Exam - Math: Using Algebraic Expressions
- Michigan Merit Exam - Math: Properties of Functions
- Michigan Merit Exam - Math: Working with Functions
- Michigan Merit Exam - Math: Lines & Linear Functions
- Michigan Merit Exam - Math: Absolute Values
- Michigan Merit Exam - Math: Inequalities
- Michigan Merit Exam - Math: Exponential & Logarithmic Functions
- Michigan Merit Exam - Math: Quadratic Functions
- Michigan Merit Exam - Math: Power Functions
- Michigan Merit Exam - Math: Polynomial Functions
- Michigan Merit Exam - Math: Rational Functions
- Michigan Merit Exam - Math: Trigonometric Functions
- Michigan Merit Exam - Math: Triangles & Their Properties
- Michigan Merit Exam - Math: Triangles & Trigonometry
- Michigan Merit Exam - Math: Quadrilaterals & Their Properties
- Michigan Merit Exam - Math: Other Polygons & Their Properties
- Michigan Merit Exam - Math: Circles & Their Properties
- Michigan Merit Exam - Math: Conic Sections & Their Properties
- Michigan Merit Exam - Math: 3D Figures
- Michigan Merit Exam - Math: Comparing Area & Volume Formulas
- Michigan Merit Exam - Math: 2D & 3D Representations
- Michigan Merit Exam - Math: Congruence & Similarity
- Michigan Merit Exam - Math: Transformations & Isometries
- Michigan Merit Exam - Math: Dilations & Isometries
- Michigan Merit Exam - Math: Creating & Interpreting Plots
- Michigan Merit Exam - Math: Measures of Center & Variation
- Michigan Merit Exam - Math: The Normal Distribution
- Michigan Merit Exam - Math: Scatterplots & Correlation
- Michigan Merit Exam - Math: Linear Regression
- Michigan Merit Exam - Math: Data Collection & Analysis
- Michigan Merit Exam - Math: Probability
- Michigan Merit Exam - Math: Application & Representation
- Michigan Merit Exam - Math Flashcards