About This Chapter
Advanced Middle School Geometry - Chapter Summary
This advanced middle school geometry chapter covers important geometric proofs, formulas and theorems that are commonly taught at the middle-school level. These lessons go over concepts such as congruence and similarity and define terms like reflection, rotation and translation. You'll practice graphing transformation and see how to properly format geometric proofs. These lessons help you use the Pythagorean theorem to find distance and plot figures on a coordinate graph. After going through each lesson in the chapter, you should be able to:
- Understand congruence and similarity in geometric shapes
- Define reflection, rotation and translation
- Plot simple figures on coordinate graphs
- Find distance using the Pythagorean theorem
- Graph transformations
- Know the formula for finding scale factors
- Assess trigonometric ratios and similarity
- Format geometric proofs
The lessons in this chapter are typically less than 10 minutes in length, which helps you quickly review essential geometry concepts in bite-sized chunks. Our expert instructors use straightforward definitions and support them with practice problems and examples so you can easily remember them. After you finish a lesson, you can make sure you fully understand what you've covered by taking the accompanying self-assessment quiz. You can access the chapter material at any time and on any computer or mobile device, which makes the learning process flexible and convenient.
1. Congruence in Geometric Shapes
Watch this video lesson to learn how you can determine whether two shapes are congruent or not. You will learn what the one criterion is when determining congruency between two shapes.
2. Reflection, Rotation & Translation
This lesson will define reflection, rotation, and translation as they relate to math. It will also show you an example of each one so that you can perform these transformations on your own.
3. Plotting Simple Figures on Coordinate Graphs
One of the most basic parts of geometry is learning how to plot simple figures onto a coordinate graph. In this lesson, we learn how to do that, as well as calculate the area and length of the figures we sketched.
4. Finding Distance with the Pythagorean Theorem
How much faster is it to cut the corners in a race around the block? In this lesson, review the Pythagorean Theorem, and figure out how to solve without a right triangle.
5. Similarity in Geometric Shapes
View this lesson to learn how you can determine whether shapes are similar. Find out how to use the one rule that tells you when your two shapes are geometrically similar.
6. Transformations in Math: Definition & Graph
In geometry, transformation refers to the movement of objects in the coordinate plane. This lesson will define and give examples of each of the four common transformations and end with a quiz to make sure you are moving in the right direction.
7. What is a Scale Factor? - Definition, Formula & Examples
How does a carpenter know the correct length of a room on a blueprint? How can a graphic designer tell if an enlarged picture will be distorted? Learn what a scale factor is and how you can use it in this article!
8. Trigonometric Ratios and Similarity
Where do terms like sine, cosine and tangent come from? In this lesson, we'll learn about how similarity with right triangles leads to trigonometric ratios.
9. 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.
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