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Searching for ## Congruence, Similarity, and Symmetry

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Algebra Foundations

You get to learn what it means for triangles to be congruent or similar and use some theorems to decide.

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After completing this tutorial, you will be able to complete the following:

- Define the similarity of triangles.

What is the definition of similar triangles? If triangle ABC and DEF are similar, how do we write this with mathematical symbols?

~ Triangles whose corresponding angles are congruent are called similar triangles. When triangle ABC and DEF are similar, we write ABC ~ DEF. The symbol ~ is called the similarity symbol.

How do the corresponding sides of similar triangles compare to one another?

~ The corresponding side lengths of similar triangles are proportional.

What is the similarity ratio between two similar triangles?

~ The ratio between corresponding side lengths of similar triangles is called the similarity ratio.

How can you determine whether two triangles are similar?

~ One way to identify similar triangles is to compare their corresponding interior angles. If all corresponding angles are congruent, then the triangles are similar.

Are two congruent triangles necessarily similar triangles? Are two similar triangles necessarily congruent triangles?

~ Two congruent triangles are necessarily similar triangles because their corresponding interior angles are congruent. Two similar triangles might not be congruent. This is because the lengths of corresponding sides of similar triangles are proportional and not necessarily congruent. For example, two equilateral triangles of different side lengths are similar but are not congruent.

Approximate Time | 2 Minutes |

Pre-requisite Concepts | Students should be familiar with these terms similarity ratio and similar triangles. |

Course | Algebra Foundations |

Type of Tutorial | Animation |

Key Vocabulary | similarity ratio, similar triangles, |