Triangle Similarity

Front

What is Triangle Similarity?

Back

Triangle similarity refers to the property of two triangles having the same shape but not necessarily the same size. This means that their corresponding angles are equal and the lengths of their corresponding sides are proportional.

Front

What are the criteria for triangle similarity?

Back

The criteria for triangle similarity are: 1. AA (Angle-Angle) Criterion: If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. 2. SSS (Side-Side-Side) Criterion: If the sides of one triangle are proportional to the sides of another triangle, the triangles are similar. 3. SAS (Side-Angle-Side) Criterion: If two sides of one triangle are proportional to two sides of another triangle and the included angle is equal, the triangles are similar.

Front

What does the SSS criterion state?

Back

The SSS (Side-Side-Side) criterion states that if the lengths of the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What does the AA criterion state?

Back

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

Front

What does the SAS criterion state?

Back

The SAS (Side-Angle-Side) criterion states that if two sides of one triangle are proportional to two sides of another triangle and the angle between those sides is equal, then the triangles are similar.

Front

If triangle ABC is similar to triangle DEF, and the lengths of AB and DE are 4 and 8 respectively, what is the ratio of the sides?

Back

Front

If triangle XYZ is similar to triangle PQR, and the length of side XY is 10 and side PQ is 5, what is the ratio of similarity?

Back

Front

If two triangles have a corresponding angle of 60 degrees, what can be inferred about their similarity?

Back

If two triangles have a corresponding angle of 60 degrees, it is not enough to conclude similarity. At least one more angle must be equal (AA criterion) or the sides must be proportional (SSS or SAS criteria) to establish similarity.

Front

What is the relationship between the sides of similar triangles?

Back

Front

If triangle ABC is not similar to triangle DEF, what can be said about their angles?

Back

If triangle ABC is not similar to triangle DEF, then at least one pair of corresponding angles is not equal.