About This Chapter
Below is a sample breakdown of the Similar Polygons chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.
|Day||Topics||Key Terms and Concepts Covered|
|Monday|| Ratios and Proportions: Definition and Examples; |
Geometric Mean: Definition and Formula;
Angle Bisector Theorem: Definition and Example
| Examples of proportion and ratio and their applications to real life; |
The contrast between the geometric mean and the arithmetic mean;
Identifying angle bisectors
|Tuesday|| Solving Problems Involving Proportions: Definition and Examples; |
Similar Polygons: Definition and Examples;
Similar Triangles and the AA Criterion
| Explaining proportions and calculating missing sides; |
Using same angles and similar polygons;
Similarity transformations and similar triangles
|Wednesday|| The Transitive Property of Similar Triangles; |
Triangle Proportionality Theorem: Definition and Examples
| The process of applying this property to similar triangles; |
Solving problems by applying the triangle proportionality theorem
|Thursday|| Constructing Similar Polygons: Process and Examples; |
Properties of Right Triangles: Theorems and Proofs
| The process of drawing similar polygons; |
Finding the properties of a right triangle
|Friday|| The Pythagorean Theorem: Practice and Application; |
The Pythagorean Theorem: Converse and Special Cases
| Applying the Pythagorean Theorem; |
The relationship between the law of cosines and 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.
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Other chapters within the Geometry Curriculum Resource & Lesson Plans course
- Foundations of Geometry Lesson Plans
- Logic in Mathematics Lesson Plans
- Introduction to Geometric Figures Lesson Plans
- Properties of Triangles Lesson Plans
- Triangles, Theorems & Proofs Lesson Plans
- Parallel Lines & Polygons Lesson Plans
- Quadrilaterals Lesson Plans
- Circular Arcs & Circles Lesson Plans
- Conic Sections Lesson Plans
- Geometric Solids Lesson Plans
- Analytical Geometry Lesson Plans
- Introduction to Trigonometry Lesson Plans