Skill 18: Triangle Similarity

Front

What is the definition of similar triangles?

Back

Triangles that have the same shape but may differ in size; their corresponding angles are congruent and their corresponding sides are in proportion.

Front

What does AA~ stand for in triangle similarity?

Back

AA~ stands for Angle-Angle Similarity Postulate, which states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Front

What does SSS~ stand for in triangle similarity?

Back

SSS~ stands for Side-Side-Side Similarity Postulate, which states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What does SAS~ stand for in triangle similarity?

Back

SAS~ stands for Side-Angle-Side Similarity Postulate, which states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are congruent, then the triangles are similar.

Front

If two triangles are similar, what can be said about their corresponding angles?

Back

All corresponding angles in similar triangles are congruent.

Front

If ∆ABC ~ ∆XYZ, what can be concluded about the lengths of their sides?

Back

The lengths of the corresponding sides of ∆ABC and ∆XYZ are in proportion.

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.

Front

If the sides of triangle A are 3, 4, and 5, and the sides of triangle B are 6, 8, and 10, are the triangles similar?

Back

Yes, triangle A and triangle B are similar because the sides are in proportion (3:6, 4:8, 5:10).

Front

What is the significance of the term 'congruent' in the context of triangle similarity?

Back

Congruent means that two angles or sides are equal in measure; in similar triangles, corresponding angles are congruent.

Front

How can you determine if two triangles are not similar?

Back

If the corresponding angles are not congruent or the sides are not in proportion, the triangles are not similar.