Similar Figures and Dilations

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 side lengths are proportional.

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but not its shape. It involves a center point and a scale factor.

Front

How do you determine if two figures are similar?

Back

Two figures are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.

Front

What is the scale factor in a dilation?

Back

The scale factor is the ratio of the lengths of two corresponding sides of similar figures. It indicates how much the figure is enlarged or reduced.

Front

What is the relationship between the side lengths of similar figures?

Back

The ratios of the lengths of corresponding sides of similar figures are equal.

Front

What does it mean for a transformation to preserve congruence?

Back

A transformation preserves congruence if it maintains the size and shape of a figure, meaning the original figure and the transformed figure are identical.

Front

Which transformations do NOT preserve congruence?

Back

Transformations such as dilation (with a scale factor other than 1) do not preserve congruence, as they change the size of the figure.

Front

What is the formula for finding the scale factor when dilating a figure?

Back

The scale factor can be found using the formula: Scale Factor = Length of Image Side / Length of Corresponding Original Side.

Front

If two triangles are similar, what can be said about their angles?

Back

If two triangles are similar, their corresponding angles are equal.

Front

How can you use proportions to solve for unknown side lengths in similar figures?

Back

You can set up a proportion using the lengths of corresponding sides and solve for the unknown length using cross-multiplication.