About This Chapter
Symmetry, Similarity & Congruence in Geometry- Chapter Summary
The informative lessons in this chapter make it easy to find out how much you know about symmetry, similarity and congruence. Brush up on your knowledge of geometry topics such as:
- Congruency between shapes
- Rules on determining the similarity of shapes
- Line symmetry and rotational symmetry
- Examples of reflection, rotation and translation
- How to use the Pythagorean theorem
- How to determine parallel lines
- Formulas for coordinate geometry
- Euclid's work with mathematical problems
Simplify your studying process by watching the video lessons and reading the text transcripts that are found in this chapter when it is convenient for you. If you are ever stuck on any lesson or concept within a lesson, you can reach out to our knowledgeable instructors. They are here to help you and answer any questions about the chapter's material.
1. 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.
2. 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.
3. Line and Rotational Symmetries of 2-D Shapes
One of the most important concepts in geometry is the idea of symmetry. But what does it actually mean? This lesson explains the difference between line symmetry and rotational symmetry.
4. Reflection, Rotation & Translation
This lesson will define reflection, rotation, and translation as they relate to math. It will also show you an example of each one so that you can perform these transformations on your own.
5. 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.
6. 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.
7. Parallel Lines: How to Prove Lines Are Parallel
Watch this video lesson to learn how you can prove that two lines are parallel just by matching up pairs of angles. Learn which angles to pair up and what to look for.
8. Coordinate Geometry: Definition & Formulas
In this lesson we'll define coordinate geometry and learn about formulas that are commonly used in coordinate geometry. You can then take a brief quiz to see what you learned.
9. Methods & Tools for Making Geometric Constructions
Did you know that it's possible to do math without using numbers? This is exactly what Euclid did when he showed how to solve mathematical problems by drawing them out instead of with numbers.
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