Similarity Basics

Front

What is similarity in geometry?

Back

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

Front

What does the term 'scale factor' mean?

Back

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

Front

How does a dilation affect the size of a polygon?

Back

A dilation changes the size of a polygon but does not change its shape. The angles remain the same, while the sides are multiplied by the scale factor.

Front

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

Back

The corresponding angles of similar triangles are equal.

Front

If two figures are similar, what can be said about their corresponding sides?

Back

The corresponding sides of similar figures are proportional.

Front

What is the relationship between the perimeters of similar figures?

Back

The ratio of the perimeters of similar figures is equal to the ratio of their corresponding sides.

Front

If the scale factor from triangle ABC to triangle DEF is 3/2, what does this mean?

Back

It means that each side of triangle DEF is 1.5 times the length of the corresponding side of triangle ABC.

Front

What is the scale factor from triangle XYZ to triangle PQR if the sides of XYZ are 4, 6, and 8 and the sides of PQR are 2, 3, and 4?

Back

The scale factor is 1/2, as each side of triangle PQR is half the length of the corresponding side of triangle XYZ.

Front

How do you find the missing side of similar figures?

Back

To find the missing side, set up a proportion using the lengths of the corresponding sides of the similar figures.

Front

If triangle ABC is similar to triangle DEF and the length of side AB is 6 and side DE is 9, what is the scale factor?

Back

The scale factor is 3/2, as 9 divided by 6 equals 3/2.