Geometry - Similarity

Front

What is similarity in geometry?

Back

Similarity in geometry refers to the relationship between two shapes that have the same shape but may differ in size. The corresponding angles are equal, and the lengths of corresponding sides are proportional.

Front

What are the criteria for triangle similarity?

Back

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

Front

What does AA stand for in triangle similarity?

Back

AA stands for Angle-Angle. If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Front

What does SAS stand for in triangle similarity?

Back

SAS stands for Side-Angle-Side. If two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, the triangles are similar.

Front

What does SSS stand for in triangle similarity?

Back

SSS stands for Side-Side-Side. If the lengths of the corresponding sides of two triangles are proportional, the triangles are similar.

Front

If two triangles have one angle equal and the sides including that angle are proportional, what can be concluded?

Back

The triangles are similar by the SAS criterion.

Front

If two triangles have two angles equal, what can be concluded?

Back

The triangles are similar by the AA criterion.

Front

Can two triangles be similar if they do not have any equal angles?

Back

No, two triangles cannot be similar if they do not have any equal angles.

Front

If two triangles are similar, how do their perimeters compare?

Back

The perimeters of similar triangles are proportional to the lengths of their corresponding sides.

Front

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

Back

The areas of two similar triangles are proportional to the square of the lengths of their corresponding sides.