Dilation & Similarity

Front

What is dilation in geometry?

Back

Dilation is a transformation that alters the size of a figure but keeps its shape the same, using a scale factor.

Front

What is a scale factor?

Back

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

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, meaning their corresponding angles are equal and their corresponding sides are in proportion.

Front

Define proportion in mathematics.

Back

A proportion is an equation that states that two ratios are equal.

Front

If triangle ABC is dilated by a scale factor of 2, what happens to its sides?

Back

The lengths of the sides of triangle ABC will be doubled.

Front

What is the similarity ratio?

Back

The similarity ratio is the ratio of the lengths of corresponding sides of two similar figures.

Front

If the sides of two similar triangles are in the ratio 1:4, what is the ratio of their perimeters?

Back

The ratio of their perimeters will also be 1:4.

Front

How do you find the scale factor when given two points A (x1, y1) and A' (x2, y2)?

Back

The scale factor can be found by dividing the coordinates of A' by the coordinates of A: scale factor = (x2/x1) = (y2/y1).

Front

What is the relationship between the areas of two similar figures?

Back

The ratio of their areas is the square of the similarity ratio.

Front

If triangle DEF has a perimeter of 30 and is similar to triangle ABC with a perimeter of 20, what is the ratio of their perimeters?

Back

The ratio of their perimeters is 30:20, which simplifies to 3:2.