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, 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, 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, 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

How can you determine if two triangles are not similar?

Back

If none of the similarity criteria (AA~, SSS~, SAS~) are satisfied, the triangles are not similar.

Front

Example of AA~: If Triangle A has angles 30° and 60°, and Triangle B has angles 30° and 60°, are they similar?

Back

Yes, Triangle A and Triangle B are similar by AA~.

Front

Example of SSS~: If Triangle A has sides 3 cm, 4 cm, and 5 cm, and Triangle B has sides 6 cm, 8 cm, and 10 cm, are they similar?

Back

Yes, Triangle A and Triangle B are similar by SSS~.

Front

Example of SAS~: If Triangle A has sides 5 cm, 12 cm, and an included angle of 60°, and Triangle B has sides 10 cm, 24 cm, and an included angle of 60°, are they similar?

Back

Yes, Triangle A and Triangle B are similar by SAS~.

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.