About This Chapter
Geometric Shapes & Principles - Chapter Summary
Let this chapter be your study guide as you dust the cobwebs out of your mind and refresh yourself on the basics of geometry. Review the properties of polygons and 3-dimensional shapes and see how to deconstruct a 3-dimensional figure into a 2-dimensional net. Once you complete this chapter, you should be ready to do the following:
- Describe basic shapes in geometry
- Identify the applications of the Pythagorean theorem
- Analyze polygons and regular polygons
- Identify angles, lines, and points
- Graph math transformations
- Recognize symmetry in mathematics
- Explain the properties of similar and congruent shapes
- Point out the corresponding parts of congruent triangles
- Offer examples of 3D geometric shapes
- Explain isometric drawings and nets of 3D figures
This convenient and user-friendly chapter is available online 24/7 and is accessible via a computer or mobile device. After reviewing the engaging text and video lessons, use the corresponding quizzes to assess your understanding. Return to any of the geometric shape concepts you are unsure about though the links in the quiz results.
1. 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.
2. 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.
3. What Are Polygons? - Definition and Examples
Watch this video lesson to see how the shapes that you grew up with are all related. Learn why the shapes of bricks, stars, and street blocks are considered polygons while the sun, moon, and rolling hills are not.
4. Regular Polygons: Definition & Parts
What makes a polygon a polygon? And what shapes are considered polygons? In this lesson, find out the answers to these questions and more as we learn all about polygons and their parts.
5. 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.
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 Symmetry in Math? - Definition & Concept
Symmetry occurs in many areas of mathematics. This lesson explains symmetry in math and explores the three basic types of symmetry: rotational symmetry, reflection symmetry, and point symmetry.
8. Properties of Congruent and Similar Shapes
In this lesson, we'll look at triangles, rectangles and other shapes that share properties. This includes both congruent and similar shapes. We'll also practice identifying the missing properties of these shapes.
9. Congruence Proofs: Corresponding Parts of Congruent Triangles
Congruent triangles have congruent sides and angles, and the sides and angles of one triangle correspond to their twins in the other. In this lesson, we'll try practice with some geometric proofs based around this theorem.
10. 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.
11. What is an Isometric Drawing? - Definition & Examples
This lesson will explain how isometric drawings address the challenges of depicting 3D objects. You'll see some examples and may become inspired to create your own! After the lesson, you can take a brief quiz to see what you've learned.
12. Nets of 3-Dimensional Figures
After watching this video lesson, you will be able to deconstruct a 3-dimensional figure into its 2-dimensional net. Learn what kind of shape you will get after opening and flattening your 3-dimensional figure.
13. Counting Faces, Edges & Vertices of Polyhedrons
After watching this video lesson, you will be able to count how many faces, edges, and vertices a polyhedron has. Also, you will learn how the number of faces, edges, and vertices are related.
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