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 the ratios of the lengths of their corresponding sides are proportional.

Front

How can you determine if two triangles are similar?

Back

Two triangles are similar if they satisfy one of the following criteria: AA (Angle-Angle) criterion, SSS (Side-Side-Side) similarity criterion, or SAS (Side-Angle-Side) similarity criterion.

Front

What is the AA criterion for triangle similarity?

Back

The AA criterion 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 criterion for triangle similarity?

Back

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

Front

What is the SAS criterion for triangle similarity?

Back

The SAS criterion states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

What does it mean for the ratios of corresponding sides to be equal?

Back

It means that the lengths of the sides of one figure divided by the lengths of the corresponding sides of another figure yield the same constant value, indicating similarity.

Front

How do you find a missing side length in similar figures?

Back

To find a missing side length in similar figures, set up a proportion using the lengths of the corresponding sides and solve for the unknown.

Front

What is the relationship between the areas of similar figures?

Back

The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.

Front

What is a scale factor in the context of similar figures?

Back

The scale factor is the ratio of the lengths of corresponding sides of two similar figures, indicating how much one figure is enlarged or reduced compared to the other.

Front

Can two figures be similar if their corresponding sides are not in proportion?

Back

No, two figures cannot be similar if the ratios of their corresponding sides are not equal.