About This Chapter
Who's it for?
Anyone who needs help understanding high school geometry material will benefit from taking this course. You will be able to grasp the subject matter faster, retain critical knowledge longer and earn better grades. You're in the right place if you:
- Have fallen behind in understanding proportions and similar polygons.
- Need an efficient way to learn about similar polygons.
- Learn best with engaging auditory and visual tools.
- Struggle with learning disabilities or learning differences, including autism and ADHD.
- Experience difficulty understanding your teachers.
- Missed class time and need to catch up.
- Can't access extra math learning resources at school.
How it works:
- Start at the beginning, or identify the topics that you need help with.
- Watch and learn from fun videos, reviewing as needed.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Submit questions to one of our instructors for personalized support if you need extra help.
- Verify you're ready by completing the Similar Polygons chapter exam.
Why it works:
- Study Efficiently: Skip what you know, review what you don't.
- Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
- Be Ready on Test Day: Use the Similar Polygons chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any relevant question. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students will review:
In this chapter, you'll learn the answers to questions including:
- How do you define ratios and proportions?
- What is the formula for the geometric mean?
- How does the angle bisector theorem work?
- How do you solve problems with proportions?
- What are similar polygons, and how do you construct them?
- How do you use the angle-angle (AA) criterion to prove two triangles are similar?
- What is unique to the transitive property of similar triangles?
- How does the triangle proportionality theorem work?
- What are the major properties of right triangles?
- What are some real-life uses for the Pythagorean Theorem?
1. Ratios and Proportions: Definition and Examples
Watch this video lesson to learn how ratios and proportions are related. Also, learn how ratios and proportions are used in real life and how you can apply them to yours.
2. Geometric Mean: Definition and Formula
Watch this video lesson to learn how different the geometric mean is from the arithmetic mean, or average, that we are all so familiar with. Learn in what circumstance the geometric mean is preferred. Also, learn the formula and how to use it.
3. 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.
4. Solving Problems Involving Proportions: Definition and Examples
Learn how you can use proportions to find missing sides and how to increase or decrease the sizes of objects to create models of them in this video lesson.
5. 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.
6. 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.
7. 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.
8. Constructing Similar Polygons
This lesson will teach you how to construct similar polygons, which are very useful in many quantitative fields. You'll learn that all of this has something to do with, of all things, snowflakes!
9. Properties of Right Triangles: Theorems & Proofs
In this lesson, you will learn about the properties of and theorems associated with right triangles, which have a wide range of applications in math and science. Specifically, we will discuss and prove the Pythagorean theorem and the right triangle altitude theorem. Let's get started.
10. 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.
11. The Pythagorean Theorem: Converse and Special Cases
The Pythagorean Theorem is a famous theorem for right triangles. Watch this video to learn how the Pythagorean Theorem relates to the law of cosines and how the converse of the Pythagorean Theorem can help you identify right triangles.
12. What is a Cuboid Shape? - Definition, Area & Properties
The cuboid is one of the most common shapes in the environment around us. In this lesson, we will learn what a cuboid shape is and how to find its volume and surface area.
13. Dodecagon: Sides, Area & Angles
A dodecagon is a polygon with twelve sides and twelve angles. In this lesson, you will learn about this polygon - its sides, angles, and how to compute the area. A quiz will follow the lesson.
14. What is a Pentagon? - Shape, Area & Definition
This lesson will prepare you to work with pentagons by teaching you the definition, description of the geometric shape, and the formula for finding its area.
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Other chapters within the High School Geometry: Help and Review course
- Foundations of Geometry: Help and Review
- Logic in Mathematics: Help and Review
- Introduction to Geometric Figures: Help and Review
- Properties of Triangles: Help and Review
- Triangles, Theorems and Proofs: Help and Review
- Parallel Lines and Polygons: Help and Review
- Quadrilaterals: Help and Review
- Circular Arcs and Circles: Help and Review
- Conic Sections: Help and Review
- Geometric Solids: Help and Review
- Analytical Geometry: Help and Review
- Introduction to Trigonometry: Help and Review