Dilation Transformations and Similarity

This lesson covers similarity transformations, focusing on dilations. It explains how to identify and verify similarity transformations, and how to determine if a dilation is an enlargement or reduction. The lesson also details how to calculate the scale factor using side lengths, including the use of diagonals and the Pythagorean theorem. Finally, it discusses verifying similarity by comparing side ratios and angle congruence.

What is the primary objective of lesson 7.6?

• To identify and verify similarity transformations

• To learn about congruence transformations

• To explore linear transformations

• To understand rotational symmetry

What does a dilation transformation do to a figure?

• It rotates the figure

• It translates the figure

• It reflects the figure

• It enlarges or reduces the figure proportionally

What is the scale factor in a dilation?

• The angle of rotation in the transformation

• The difference in area between the image and the pre-image

• The ratio of a length on the image to a corresponding length on the pre-image

• The ratio of the perimeter of the image to the pre-image

If the scale factor is greater than one, what type of transformation has occurred?

• Translation

• Reflection

• Enlargement

• Reduction

How do you determine if a dilation is an enlargement or a reduction?

• By counting the number of sides in the image

• By measuring the angles of the image

• By checking if the scale factor is greater than or less than one

• By comparing the areas of the image and pre-image

In the example of enlargement, what was the scale factor calculated?

• 2

• 3

• 1

• 0.5

What is the scale factor if a figure is reduced in size?

• Greater than one

• Less than zero

• Equal to one

• Between zero and one

When horizontal or vertical segments are not available, what method can be used to find the scale factor?

• Using the distance formula or Pythagorean theorem

• Calculating the area

• Measuring the angles

• Counting the number of sides

What is necessary to verify that a dilation produces a similar figure?

• The figures must have the same area

• The figures must have the same perimeter

• The ratios of all corresponding sides must be equal

• The figures must be congruent

What should be checked to ensure two triangles are similar?

• Their colors

• Their side lengths and angle measures

• Their perimeters

• Their areas