Similar Triangles Proofs

Front

What are 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 is the AA criterion for similarity?

Back

If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar (AA ~).

Front

What is the SSS criterion for similarity?

Back

If the lengths of the corresponding sides of two triangles are in proportion, then the triangles are similar (SSS ~).

Front

What is the SAS criterion for similarity?

Back

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 (SAS ~).

Front

What are corresponding angles?

Back

Angles that are in the same position in different triangles when the triangles are positioned similarly.

Front

What are corresponding sides?

Back

Sides that are in the same relative position in different triangles.

Front

What is the Reflexive Property?

Back

A property stating that any geometric figure is congruent to itself, often used in proofs.

Front

What is the significance of the Alt. Int. Angles theorem?

Back

If two parallel lines are cut by a transversal, then each pair of alternate interior angles is equal.

Front

What is the relationship between similar triangles and proportionality?

Back

In similar triangles, the ratios of the lengths of corresponding sides are equal.

Front

How can you prove triangles are similar using angle-angle (AA) similarity?

Back

By showing that two angles of one triangle are equal to two angles of another triangle.