Ch 7: High School Geometry: Similar Polygons

Watch geometry video lessons and learn all about similar polygons, including theorems, constructions, real-life applications and more. Take brief self-assessment quizzes to gauge your comprehension of the material.

Similar Polygons - Chapter Summary and Learning Objectives

What do similar polygons have in common? You can learn all about the theorems, proportions, properties and constructions for working with triangles. Don't be surprised if you discover some applications for everyday life. In this chapter, you can meet the AAA postulate, the AA criterion and the transitive property of similar triangles while learning to prove theorems and converse theorems in addition to identifying special-case scenarios. After completing these lessons, you should be able to:

• Characterize proportion and ratio
• Provide examples of solutions involving proportions
• Identify similar polygons
• Establish the AA criterion while using the properties of similarity transformations
• Understand the transitive property of similar triangles
• Apply the Triangle Proportionality Theorem
• Give examples of similar polygon constructions
• Supply theorem proofs about median of right triangles
• Apply the Pythagorean Theorem
• Supply the proof of the converse Pythagorean Theorem and describe special instances of the Theorem

Video Objective
Ratio, Proportion and Geometric Mean Define ratio and proportion. Define and state theorems about proportions and geometric mean.
Solving Problems Involving Proportions Define proportional segments. Explain how to solve problems involving proportions. Provide examples.
Similar Polygons: Definition and Examples Define similar polygons. Provide examples. State the AAA postulate.
Similar Triangles and the AA Criterion Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
The Transitive Property of Similar Triangles Discuss the transitive property of similar triangles.
Triangle Proportionality Theorem Define the Triangle Proportionality Theorem. Explain how to divide a triangle proportionally. Provide examples. Describe how to construct a segment proportional to three given line segments.
Constructing Similar Polygons Explain how to construct a polygon similar to a given polygon. Provide examples.
Properties of Right Triangles Use theorems involving an altitude of a right triangle. Prove theorem about median of right triangle.
The Pythagorean Theorem: Practice and Application Learn about the Pythagorean Theorem and its real-life applications.
The Pythagorean Theorem: Converse and Special Cases Prove the converse of the Pythagorean Theorem. Identify special cases of the Pythagorean Theorem.

13 Lessons in Chapter 7: High School Geometry: Similar Polygons
Test your knowledge with a 30-question chapter practice test
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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