Dilations, Similarity, Slope

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

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 proportional.

Front

What is the relationship between the angles of similar figures?

Back

All corresponding angles in similar figures are congruent (equal in measure).

Front

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

Back

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

Front

What is the formula for slope?

Back

The slope (m) of a line is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What is the slope of a line that rises 5 units and runs 4 units?

Back

The slope of the line is 5/4.

Front

What is the slope of a line that falls 5 units and runs 4 units?

Back

The slope of the line is -5/4.

Front

If two lines are parallel, what can you say about their slopes?

Back

If two lines are parallel, their slopes are equal.

Front

If two lines are perpendicular, what can you say about their slopes?

Back

If two lines are perpendicular, the product of their slopes is -1.