Triangle Similarity Theorems

Front

What is the Triangle Similarity Theorem?

Back

The Triangle Similarity Theorem states that if two triangles have corresponding angles that are equal, then the triangles are similar, meaning their corresponding sides are in proportion.

Front

What is the AA (Angle-Angle) Criterion for Triangle Similarity?

Back

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

Front

What is the SSS (Side-Side-Side) Criterion for Triangle Similarity?

Back

The SSS Criterion states that if the lengths of the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What is the SAS (Side-Angle-Side) Criterion for Triangle Similarity?

Back

The SAS 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 △ABC ~ △DEF, what can be said about their corresponding sides?

Back

If △ABC is similar to △DEF, then the lengths of the corresponding sides are in proportion.

Front

If the angles of triangle A are 30°, 60°, and 90°, what are the angles of a similar triangle?

Back

A similar triangle will also have angles of 30°, 60°, and 90°.

Front

How do you determine if two triangles are similar using their angles?

Back

Two triangles are similar if all three pairs of corresponding angles are equal.

Front

What is the relationship between the areas of two similar triangles?

Back

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Front

If the sides of triangle A are 3, 4, and 5, and triangle B is similar to triangle A with a side length of 6, what is the length of the other sides of triangle B?

Back

The sides of triangle B will be 6, 8, and 10, maintaining the same ratio as triangle A.

Front

What does it mean for triangles to be congruent?

Back

Triangles are congruent if they have the same size and shape, meaning all corresponding sides and angles are equal.