Similar Triangles Theorems

Front

What does the Side-Angle-Side Similarity (SAS ~) Theorem state?

Back

If two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are similar.

Front

What does the Side-Side-Side Similarity (SSS ~) Theorem state?

Back

If the corresponding sides of two triangles are proportional, then the triangles are similar.

Front

What is the AA similarity criterion?

Back

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

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 proportional.

Front

What is the relationship between the angles in similar triangles?

Back

The corresponding angles in similar triangles are equal.

Front

What is the relationship between the sides in similar triangles?

Back

The corresponding sides in similar triangles are proportional.

Front

How can you prove that two triangles are similar using the SAS criterion?

Back

Show that two sides of one triangle are proportional to two sides of another triangle and that the included angles are congruent.

Front

How can you prove that two triangles are similar using the SSS criterion?

Back

Show that the lengths of the corresponding sides of the two triangles are proportional.

Front

What is a similarity statement?

Back

A statement that indicates that two figures are similar, often written in the form △ABC ~ △DEF.

Front

What is the importance of the included angle in the SAS similarity theorem?

Back

The included angle must be congruent for the triangles to be considered similar under the SAS criterion.