Similarity And Dilations

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. This means their corresponding angles are equal and their corresponding sides are in proportion.

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but keeps its shape. It can be an enlargement (making the figure larger) or a reduction (making the figure smaller).

Front

If triangle ABC is dilated by a scale factor of 2, how does the length of each side change?

Back

Each side of triangle ABC will be multiplied by 2, making the triangle larger while maintaining its shape.

Front

What is the scale factor in a dilation?

Back

The scale factor is the ratio of the length of a side of the image to the length of the corresponding side of the original figure. It determines how much the figure is enlarged or reduced.

Front

How do you find the missing side of similar figures?

Back

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

Front

If two triangles are similar and the lengths of one triangle's sides are 4, 6, and 8, what could be the lengths of the corresponding sides of the other triangle if the scale factor is 3?

Back

The corresponding sides would be 12 (4x3), 18 (6x3), and 24 (8x3).

Front

What is the relationship between the angles of similar figures?

Back

The corresponding angles of similar figures are equal.

Front

If a triangle has vertices at (2, 3), (4, 5), and (6, 7), what are the coordinates of the triangle after a dilation with a scale factor of 1/2?

Back

The new coordinates will be (1, 1.5), (2, 2.5), and (3, 3.5).

Front

What happens to the area of a figure when it is dilated by a scale factor of k?

Back

The area of the figure is multiplied by k^2. For example, if the scale factor is 2, the area increases by a factor of 4.

Front

If two similar rectangles have a length ratio of 3:5, what is the ratio of their areas?

Back

The ratio of their areas is 3^2:5^2, which simplifies to 9:25.