Honors Geometry - Similarity Criteria

Front

What is the definition of similar figures?

Back

Similar figures are shapes that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are proportional.

Front

What does the AA Similarity Criterion state?

Back

The AA (Angle-Angle) Similarity Criterion states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What does the SSS Similarity Criterion state?

Back

The SSS (Side-Side-Side) Similarity Criterion states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What does the SAS Similarity Criterion state?

Back

The SAS (Side-Angle-Side) Similarity Criterion states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

If two triangles have one angle equal and the sides including that angle are in proportion, what can be concluded?

Back

The triangles are similar by the SAS Similarity Criterion.

Front

If two triangles have two angles equal, what can be concluded?

Back

The triangles are similar by the AA Similarity Criterion.

Front

What is the relationship between the sides of similar triangles?

Back

The sides of similar triangles are proportional, meaning the ratios of the lengths of corresponding sides are equal.

Front

Can you determine similarity with only one pair of equal angles?

Back

No, one pair of equal angles is not sufficient to prove similarity; at least two pairs of equal angles are needed.

Front

What is the importance of the proportionality of sides in similar triangles?

Back

Proportionality of sides ensures that the triangles maintain their shape, allowing for the application of similarity in solving problems.

Front

How can you prove that two triangles are not similar?

Back

If the corresponding angles are not equal or the sides are not in proportion, then the triangles are not similar.