Similar figures

Front

What are similar figures?

Back

Similar figures are shapes that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are proportional.

Front

What does it mean for sides in similar figures to be proportional?

Back

It means that the ratios of the lengths of corresponding sides of the figures are equal.

Front

What is the AA (Angle-Angle) similarity postulate?

Back

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

Front

What is the SSS (Side-Side-Side) similarity theorem?

Back

The SSS theorem states that if the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

Front

What is the SAS (Side-Angle-Side) similarity theorem?

Back

The SAS theorem 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

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

Back

The corresponding angles of triangle ABC and triangle DEF are equal.

Front

If the sides of two similar triangles are in the ratio 2:3, what is the ratio of their areas?

Back

The ratio of their areas is the square of the ratio of their corresponding sides, which is 4:9.

Front

How can you determine if two triangles are similar using their angles?

Back

If two triangles have two pairs of corresponding angles that are equal, then the triangles are similar (AA postulate).

Front

What is the relationship between the lengths of corresponding sides of similar triangles?

Back

The lengths of corresponding sides of similar triangles are in proportion to each other.

Front

If triangle XYZ has sides of lengths 4, 6, and 8, and triangle PQR is similar to triangle XYZ, what could be the lengths of the sides of triangle PQR?

Back

The lengths of the sides of triangle PQR could be in the same ratio as triangle XYZ, such as 2, 3, and 4, or 8, 12, and 16.