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.

Front

What are the criteria for triangle similarity?

Back

The criteria for triangle similarity include Angle-Angle (AA), Side-Side-Side (SSS), and Side-Angle-Side (SAS).

Front

If △ABC ~ △DEF, what does this imply about their corresponding sides?

Back

If △ABC ~ △DEF, then the ratios of the lengths of their corresponding sides are equal.

Front

What is the Angle-Angle (AA) criterion for triangle similarity?

Back

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

Front

How can you determine if two triangles are similar using the SSS criterion?

Back

To determine if two triangles are similar using the SSS criterion, check if the ratios of the lengths of corresponding sides are equal.

Front

What does it mean for triangles to be similar?

Back

Triangles are similar if they have the same shape but not necessarily the same size, meaning their corresponding angles are equal and their corresponding sides are in proportion.

Front

What is the Side-Angle-Side (SAS) criterion for triangle similarity?

Back

The SAS criterion states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

Complete the similarity statement: △ABC ~ _______ if angle A = angle D and angle B = angle E.

Back

△DEF.

Front

If △WXY ~ △YZW, what can be said about their angles?

Back

If △WXY ~ △YZW, then angle W = angle Y, angle X = angle Z, and angle Y = angle W.

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 side lengths.