Determining Similarity of Figures Using Dilations and Scale Factors

This lesson teaches how to determine if two figures are similar using dilations and scale factors. It reviews the properties of similar figures, such as congruent angles and proportional sides. The lesson explains how to find and apply scale factors, using examples with triangles, trapezoids, and squares. It also covers common mistakes and methods to prove similarity through dilations.

What is a key characteristic of similar figures?

• Their corresponding angles are congruent.

• Their sides are not proportional.

• They have the same size.

• They have different shapes.

What is a common mistake students make when working with dilation problems?

• Confusing the shapes of figures.

• Misidentifying corresponding angles.

• Incorrectly finding the scale factor.

• Ignoring the size of the figures.

How do you determine the scale factor using coordinates?

• By adding the coordinates.

• By subtracting the coordinates.

• By dividing a postdilation coordinate by a predilation coordinate.

• By multiplying the coordinates.

What happens to a figure when it undergoes a dilation with a scale factor less than 1?

• The figure changes shape.

• The figure shrinks.

• The figure remains the same size.

• The figure enlarges.

How can you prove that two trapezoids are similar?

• By verifying that their scale factor is consistent across all coordinates.

• By checking if their angles are different.

• By ensuring their sides are not proportional.

• By comparing their perimeters.

What is the scale factor used to prove the similarity of squares in the example?

• 2

• 1/4

• 2.5

• 1/2

What is the main takeaway from the lesson on similar figures?

• Similar figures have different shapes.

• Dilations do not affect the size of figures.

• Scale factors are crucial in determining similarity.

• Angles are not important in similarity.