Similar polygons + dilations

Front

What is a dilation in geometry?

Back

A transformation that produces a similar figure by enlarging or reducing it based on a scale factor.

Front

What does it mean for two polygons to be similar?

Back

Two polygons are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Front

What is the scale factor in a dilation?

Back

The ratio of the lengths of corresponding sides of the original figure to the dilated figure.

Front

If a polygon is dilated by a scale factor of 2, what happens to its size?

Back

The polygon is enlarged to twice its original size.

Front

If a polygon is dilated by a scale factor of \( \frac{1}{2} \), what happens to its size?

Back

The polygon is reduced to half its original size.

Front

What is the relationship between the areas of similar polygons?

Back

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

Front

How do you determine if two triangles are similar?

Back

Two triangles are similar if they satisfy the Angle-Angle (AA) criterion, meaning two angles of one triangle are equal to two angles of another triangle.

Front

What is the effect of a dilation on the coordinates of a point (x, y)?

Back

If a point (x, y) is dilated from the origin by a scale factor k, its new coordinates will be (kx, ky).

Front

What does the term 'reduction' mean in the context of dilations?

Back

Reduction refers to a dilation with a scale factor less than 1, resulting in a smaller figure.

Front

What does the term 'enlargement' mean in the context of dilations?

Back

Enlargement refers to a dilation with a scale factor greater than 1, resulting in a larger figure.