About This Chapter
Who's it for?
This unit of our High School Geometry Homeschool course will benefit any student who is trying to learn about using angles and sides to identify similar polygons. There is no faster or easier way to learn about similar polygons. Among those who would benefit are:
- Students who require an efficient, self-paced course of study to learn about the properties of triangles and to solve problems that involve proportions.
- Homeschool parents looking to spend less time preparing lessons and more time teaching.
- Homeschool parents who need a math curriculum that appeals to multiple learning types (visual or auditory).
- Gifted students and students with learning differences.
How it works:
- Students watch a short, fun video lesson that covers a specific unit topic.
- Students and parents can refer to the video transcripts to reinforce learning.
- Short quizzes and the Similar Polygons unit exam confirm understanding or identify any topics that require review.
Similar Polygons Unit Objectives:
- Find the transitive property of similar triangles.
- Learn about proportional segments.
- Identify the properties of right triangles.
- Explain the angle bisector theorem.
- Provide examples of the triangle proportionality theorem.
- Learn to apply the Pythagorean theorem.
- Prove special cases and the converse of the Pythagorean theorem.
- Establish the criteria for two triangles to be similar.
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.
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Other chapters within the High School Geometry: Homeschool Curriculum course
- Foundations of Geometry: Homeschool Curriculum
- Logic in Mathematics: Homeschool Curriculum
- Geometric Figures: Homeschool Curriculum
- Properties of Triangles: Homeschool Curriculum
- Triangles, Theorems & Proofs: Homeschool Curriculum
- Parallel Lines & Polygons: Homeschool Curriculum
- Quadrilaterals: Homeschool Curriculum
- Circular Arcs and Circles: Homeschool Curriculum
- Focus & Directrix: Homeschool Curriculum
- Geometric Solids: Homeschool Curriculum
- Analytical Geometry: Homeschool Curriculum
- Introduction to Trigonometry: Homeschool Curriculum