Similarity and Dilations Review

Front

What is the definition of similarity in geometry?

Back

Similarity in geometry refers to two figures that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are proportional.

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, some quantity. In geometry, it is the ratio of the lengths of corresponding sides of similar figures.

Front

How do you calculate the scale factor between two similar triangles?

Back

To calculate the scale factor between two similar triangles, divide the length of a side of one triangle by the length of the corresponding side of the other triangle.

Front

If Triangle ABC is dilated using a scale factor of 3, what happens to the lengths of its sides?

Back

If Triangle ABC is dilated using a scale factor of 3, each side of the triangle will be multiplied by 3, making the new triangle three times larger.

Front

What is the dilation rule for a scale factor of 1/2?

Back

The dilation rule for a scale factor of 1/2 is (x, y) → (1/2 x, 1/2 y), which reduces the size of the figure to half its original dimensions.

Front

What are the coordinates of point C' if point C(6, -12) is dilated by a scale factor of 2?

Back

The coordinates of point C' would be (12, -24) after applying the dilation rule (x, y) → (2x, 2y).

Front

What does it mean for two figures to be congruent?

Back

Two figures are congruent if they have the same shape and size, meaning their corresponding sides and angles are equal.

Front

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

Back

If Triangle ABC is similar to Triangle DEF, then their corresponding angles are equal.

Front

What is the relationship between the sides of similar figures?

Back

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

Front

How do you determine if two triangles are similar using the AA criterion?

Back

Two triangles are similar if two angles of one triangle are equal to two angles of another triangle (AA criterion).