About This Chapter
How It Works
- Identify the lessons in the textbook chapter with which you need help.
- Find the corresponding video lessons within this online chapter.
- Watch fun videos that cover the similarity topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.
You'll learn all of the geometry topics covered in the textbook chapter, including:
- Examples and the meaning of similar polygons
- Characteristics of similar and congruent shapes
- Ways to recognize and apply triangles
- How transitive property is applied in similar triangles
- The meaning of altitude, angle and median bisectors of a triangle
- Definition of the angle bisector theorem
- How to apply scale factors to volume, perimeter and area
- Uses of the triangle proportionality theorem
1. Similar Polygons: Definition and Examples
Watch this video to learn what makes two polygons similar to each other. You'll also learn the one distinguishing aspect of similar polygons and see an example of how to compare two polygons.
2. 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.
3. 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.
4. 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.
5. The Transitive Property of Similar Triangles
Watch this video lesson and you will understand what the transitive property is and how it applies to similar triangles. Watch as we apply the transitive property to three similar triangles.
6. Median, Altitude, and Angle Bisectors of a Triangle
Line segments in triangles are just clutter; they have special names and qualities depending on how they're drawn. In this lesson, we'll learn about medians, altitudes and angle bisectors.
7. Angle Bisector Theorem: Definition and Example
Watch this video lesson and learn how you can use the angle bisector theorem to help you find the lengths of missing sides. Also learn how you can identify an angle bisector just by looking at the lengths of the sides of a triangle.
8. Applying Scale Factors to Perimeter, Area, and Volume of Similar Figures
How do shapes change sizes yet retain their proportions and similarities to other shapes? In this lesson, we'll look at what a scale factor is and how to apply it. We'll consider scale factors with regards to three different aspects of similar shapes: perimeter, area and volume.
9. Triangle Proportionality Theorem
Watch this video lesson to learn all about the triangle proportionality theorem and how you can use this interesting theorem to help you solve problems. Learn how a parallel line can create sides that are proportional to each other.
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Other chapters within the Discovering Geometry An Investigative Approach: Online Help course
- Discovering Geometry Chapter 1: Introducing Geometry
- Discovering Geometry Chapter 2: Reasoning in Geometry
- Discovering Geometry Chapter 3: Using Tools of Geometry
- Discovering Geometry Chapter 4: Discovering and Proving Triangle Properties
- Discovering Geometry Chapter 5: Discovering and Proving Polygon Properties
- Discovering Geometry Chapter 6: Discovering and Proving Circle Properties
- Discovering Geometry Chapter 7: Transformations and Tessellations
- Discovering Geometry Chapter 8: Area
- Discovering Geometry Chapter 9: The Pythagorean Theorem
- Discovering Geometry Chapter 10: Volume
- Discovering Geometry Chapter 12: Trigonometry
- Discovering Geometry Chapter 13: Geometry as a Mathematical System