About This Chapter
Congruence & Similarity in Geometry - Chapter Summary
Let us guide you through video lessons explaining congruence and similarity topics. These topics will include everything from vocabulary to theorems.
In this chapter, instructors will give you the tools necessary to solve problems concerning triangles. They will teach you how to prove theorems and determine whether or not two triangles are similar. This chapter is your guide to identifying symmetry, congruence and similarity in geometric shapes. Once you've completed this chapter, you will be familiar with:
- Line of symmetry in geometric shapes
- Congruence and similarity in geometric shapes
- Applications of similar triangles
- Postulates SAS, ASA and SSS
- The LA and LL theorems
- Congruency in right and isosceles triangles
- Similarity transformations
- Congruent and similar relationships between figures
- Similar polygons
Our instructors will help you brush up on essential information about similarity and congruence. After watching engaging lesson videos, you can practice further with multiple choice quizzes. As you watch videos, read text lessons and transcripts, and take quizzes, be sure to track your progress on your personal dashboard.
1. What is a Line of Symmetry in Geometric Shapes?
After viewing this lesson, you should be able to identify shapes that have a line of symmetry in them and know how to find where this line is. A short quiz to test your knowledge will follow the lesson.
2. Congruence in Geometric Shapes
Watch this video lesson to learn how you can determine whether two shapes are congruent or not. You will learn what the one criterion is when determining congruency between two shapes.
3. Similarity in Geometric Shapes
View this lesson to learn how you can determine whether shapes are similar. Find out how to use the one rule that tells you when your two shapes are geometrically similar.
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. Triangle Congruence Postulates: SAS, ASA & SSS
When we have two triangles, how can we tell if they're congruent? They may look the same, but you can be certain by using one of several triangle congruence postulates, such as SSS, SAS or ASA.
6. Congruency of Right Triangles: Definition of LA and LL Theorems
In this lesson, we'll learn two theorems that help us prove when two right triangles are congruent to one another. The LA theorem, or leg-acute, and LL theorem, or leg-leg, are useful shortcuts for proving congruence.
7. Congruency of Isosceles Triangles: Proving the Theorem
Isosceles triangles have two equal sides. Are the base angles also equal? In this lesson, we'll prove how this is true. We'll also prove the theorem's converse.
8. Similarity Transformations in Corresponding Figures
Watch this video lesson to learn how you can tell if two figures are similar by using similarity transformations. Learn how to find the corresponding sides and angles and then how to compare them.
9. How to Prove Relationships in Figures using Congruence & Similarity
In this lesson, we'll look at similar and congruent figures and the properties that they hold. We will then look at how to use these properties to prove relationships in these figures in various examples.
10. Practice Proving Relationships using Congruence & Similarity
In geometry, if two shapes are similar they have the same shape but different sizes, while two congruent shapes have the same shape and size. In this lesson, you will learn how to prove that shapes are similar or congruent.
11. 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.
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Other chapters within the MTLE Middle Level Mathematics: Practice & Study Guide course
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- 6th-8th Grade Math: Properties of Numbers
- Number Theory & Factoring
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