Similarity Criteria

Front

What is the definition of similar triangles?

Back

Triangles that have the same shape but may differ in size; their corresponding angles are equal and their corresponding sides are in proportion.

Front

What does AA~ stand for in triangle similarity?

Back

AA~ stands for Angle-Angle similarity criterion, which states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Front

What does SSS~ stand for in triangle similarity?

Back

SSS~ stands for Side-Side-Side similarity criterion, which states that if the corresponding sides of two triangles are in proportion, the triangles are similar.

Front

What does SAS~ stand for in triangle similarity?

Back

SAS~ stands for Side-Angle-Side similarity criterion, which states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, the triangles are similar.

Front

If two triangles have one angle equal and the sides including that angle are in proportion, what similarity criterion applies?

Back

SAS~ (Side-Angle-Side similarity criterion).

Front

If two triangles have all three pairs of corresponding sides in proportion, what can be concluded?

Back

The triangles are similar by the SSS~ (Side-Side-Side similarity criterion).

Front

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

Back

The triangles are similar by the AA~ (Angle-Angle similarity criterion).

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

What is the relationship between the sides of similar triangles?

Back

The corresponding sides of similar triangles are in proportion.

Front

Can two triangles be similar if they have no angles equal?

Back

No, if no angles are equal, the triangles cannot be similar.