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Ch 15: Geometric Shapes & Properties

About This Chapter

Check out these video lessons on the properties of points, lines, angles and basic shapes. You'll review methods for calculating area, perimeter and volume, determining triangle similarity and finding the measures of missing triangle sides or angles.

Geometric Shapes & Properties - Chapter Summary

Begin your geometry review with lessons on the properties of points and lines as well as the types of angles formed by intersecting lines and transversals. You'll also compare the properties of triangles, circles and parallelograms - such as rhombuses, squares and rectangles - before reviewing formulas for their area and perimeter.

Our experienced instructors also walk you through the applications of the Pythagorean theorem, methods for proving triangle similarity and the steps involved in finding the measures of triangles' interior angles. Wrap up your geometry review with a lesson on formulas for the volume of three-dimensional shapes. Topics of instruction include:

  • Points, lines and angles
  • Basic shape properties
  • Area, perimeter and volume
  • The Pythagorean theorem
  • Triangle similarity

This chapter's short video lessons allow you to focus on the topics you're interested in studying. Start with introductory lessons if you're looking for a more comprehensive review of geometric shapes and properties, or skip ahead to lessons covering the formulas and theorems you need some extra practice working with. Sample problems are included in the videos as well as the multiple-choice lesson and chapter quizzes.

15 Lessons in Chapter 15: Geometric Shapes & Properties
Test your knowledge with a 30-question chapter practice test
Points, Lines & Angles in Geometry

1. 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.

Types of Angles: Vertical, Corresponding, Alternate Interior & Others

2. 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.

Overview of the Basic Shapes in Geometry

3. 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.

Properties of Shapes: Rectangles, Squares and Rhombuses

4. Properties of Shapes: Rectangles, Squares and Rhombuses

What's the difference between a square and a rectangle? What about a rhombus and a square? In this lesson, we'll look at the properties of these shapes.

Properties of Shapes: Triangles

5. Properties of Shapes: Triangles

Isosceles, equilateral and obtuse, oh my! These are terms for triangles. But, what do they mean? In this lesson, we'll explore the properties of triangles and take a closer look at the different types of triangles you may encounter.

Perimeter of Triangles and Rectangles

6. Perimeter of Triangles and Rectangles

Without realizing it, we calculate and use the perimeter of triangles and rectangles in regular everyday situations. Learn more about the perimeter of triangles and rectangles in this lesson, and test your knowledge with a quiz.

Area of Triangles and Rectangles

7. Area of Triangles and Rectangles

How do you find out the area of rectangles and triangles? Learn how in this lesson! We'll look at the formulas, then practice solving problems for each shape.

Circles: Area and Circumference

8. 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.

The Pythagorean Theorem: Practice and Application

9. 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.

How to Identify Similar Triangles

10. How to Identify Similar Triangles

Similar triangles have the same characteristics as similar figures but can be identified much more easily. Learn the shortcuts for identifying similar triangles here and test your ability with a quiz.

Applications of Similar Triangles

11. Applications of Similar Triangles

Similar triangles are used to solve problems in everyday situations. Learn how to solve with similar triangles here, and then test your understanding with a quiz.

Angles and Triangles: Practice Problems

12. 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.

Vertical Angles & Complementary Angles: Definition & Examples

13. Vertical Angles & Complementary Angles: Definition & Examples

Special angles make your life easier. Learn how you can use the properties of special angles to help you find the measurements of missing angles in this video lesson.

Overview of Three-dimensional Shapes in Geometry

14. 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.

How to Calculate the Volumes of Basic Shapes

15. How to Calculate the Volumes of Basic Shapes

Squares pegs = square holes. Triangular pegs = triangular holes. But where does a sphere go? In this lesson, review volumes of common shapes while contrasting a sphere and a cylinder - after all, they both go into the circular hole... right?

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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