Dilations & Similarity Review

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but not its shape, using a scale factor.

Front

Define scale factor in the context of dilations.

Back

The scale factor is a number that scales, or multiplies, the dimensions of a figure during a dilation.

Front

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

Back

All dimensions of the triangle are multiplied by 2, making it twice as large.

Front

What does it mean for two figures to be similar?

Back

Two figures are similar if they have the same shape but may differ in size, meaning their corresponding angles are equal and their corresponding sides are proportional.

Front

How do you find the scale factor between two similar figures?

Back

The scale factor can be found by dividing the length of a side of one figure by the corresponding side of the other figure.

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 from triangle ABC to triangle DEF?

Back

The scale factor is 2, since 8 cm / 4 cm = 2.

Front

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

Back

The ratio of their areas is the square of the scale factor.

Front

If the scale factor is 1/2, how does the area of the dilated figure compare to the original?

Back

The area of the dilated figure is 1/4 of the area of the original figure.

Front

How do you perform a dilation on a point (x, y) with a scale factor k?

Back

The new coordinates after dilation are (kx, ky).

Front

What is the formula for finding the missing side length in similar triangles?

Back

If triangle ABC is similar to triangle DEF, then (AB/DE) = (BC/EF) = (AC/DF).