Similarity and Dilations Flashcard Review

Front

What is similarity in geometry?

Back

Similarity in geometry refers to two shapes that have the same shape but may differ in size. 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 shape but not its shape. It involves a center of dilation and a scale factor.

Front

What is the scale factor in a dilation?

Back

The scale factor is a number that scales, or multiplies, the dimensions of a shape during a dilation. A scale factor greater than 1 enlarges the shape, while a scale factor between 0 and 1 reduces it.

Front

How do you find the coordinates of a dilated point?

Back

To find the coordinates of a dilated point, multiply the original coordinates by the scale factor. If the center of dilation is at the origin, the new coordinates (x', y') are given by (kx, ky), where k is the scale factor.

Front

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

Back

If two shapes are similar, their corresponding angles are equal.

Front

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

Back

If two shapes are similar, the lengths of their corresponding sides are proportional.

Front

What is the formula for finding the scale factor between two similar shapes?

Back

The scale factor can be found by dividing the length of a side of the larger shape by the length of the corresponding side of the smaller shape.

Front

Given two similar triangles, if the sides of the first triangle are 4, 6, and 8, and the longest side of the second triangle is 12, what is the scale factor?

Back

The scale factor is 12/8 = 1.5.

Front

What is the center of dilation?

Back

The center of dilation is a fixed point in the plane about which all points are expanded or contracted during a dilation.

Front

If a point A(2, 3) is dilated by a scale factor of 2 about the origin, what are the coordinates of A'?

Back

A' will be (2*2, 3*2) = (4, 6).