Triangle Similarity

Front

What is Triangle Similarity?

Back

Triangle similarity refers to the relationship between two triangles that have the same shape but may differ in size. This means that their corresponding angles are equal and 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, 2) SSS (Side-Side-Side) Criterion, 3) SAS (Side-Angle-Side) Criterion.

Front

What does the AA criterion state?

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 does the SSS criterion state?

Back

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

Front

What does the SAS criterion state?

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

Are all angles in similar triangles congruent?

Back

Yes, all corresponding angles in similar triangles are congruent.

Front

If two figures are similar, what can be said about their corresponding sides?

Back

If two figures are similar, their corresponding sides are proportional.

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

Can two triangles be similar if only one angle is known to be equal?

Back

No, two triangles cannot be proven similar with only one angle known to be equal; at least two angles must be equal (AA criterion).

Front

If triangle ABC is similar to triangle DEF, what can be said about their corresponding sides?

Back

If triangle ABC is similar to triangle DEF, then the ratio of side AB to side DE is equal to the ratio of side BC to side EF, and the ratio of side AC to side DF.