Review dilations and similarity

Front

What is a dilation in geometry?

Back

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. It is defined by a scale factor.

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, some quantity. In dilations, it determines how much larger or smaller the image will be compared to the original.

Front

If the scale factor is 2, what happens to the dimensions of the original figure?

Back

The dimensions of the original figure are doubled.

Front

What does it mean for two figures to be similar?

Back

Two figures are similar if they have the same shape but not necessarily the same size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

How do you find the missing side length in similar triangles?

Back

Use the property of proportions: if two triangles are similar, the ratios of the lengths of their corresponding sides are equal.

Front

If triangle ABC is similar to triangle DEF, and the length of side AB is 4 cm and side DE is 8 cm, what is the scale factor?

Back

The scale factor is 2.

Front

What is the formula for finding the area of a triangle?

Back

Area = 1/2 * base * height.

Front

If the scale factor of a dilation is 1/2, how does it affect the area of the figure?

Back

The area of the figure is reduced by a factor of (1/2)^2 = 1/4.

Front

What is the relationship between the angles of similar figures?

Back

The corresponding angles of similar figures are equal.

Front

How do you solve for a missing side length using proportions?

Back

Set up a proportion using the lengths of the corresponding sides and solve for the unknown.