Explore Dilations, Similarity, and Slope Concepts

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

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, and their corresponding angles are congruent.

Front

How do you find the slope of a line?

Back

Slope is found by counting the 'rise' (vertical change) over the 'run' (horizontal change) between two points on the line.

Front

What is the scale factor in a dilation?

Back

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

Front

Are corresponding angles in similar triangles congruent?

Back

Yes, all corresponding angles in similar triangles are congruent.

Front

If triangle ABC is similar to triangle DEF, what can be said about their corresponding sides?

Back

The lengths of the corresponding sides of similar triangles are proportional.

Front

What is the relationship between the angles of a triangle and its dilated image?

Back

The measures of the angles in a triangle remain the same after dilation.

Front

If the scale factor of a dilation is 3, how does it affect the side lengths of a triangle?

Back

Each side length of the triangle is multiplied by 3.

Front

What is the formula for calculating slope between two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

If two triangles have sides in the ratio 2:3, are they similar?

Back

Yes, if their corresponding angles are also congruent, they are similar.