Dilation and Similarity Concepts

This lesson focuses on the fundamental theorem of similarity (FTS) and its application in graphing dilations. The teacher reviews key concepts from Module 3, including how dilations change size but not shape, and the importance of scale factors and centers in transformations. The lesson includes exercises on determining scale factors, graphing dilations, and using fractional scale factors. Students are encouraged to use the dilation equation and Rule 5 to simplify calculations. The lesson concludes with instructions for a problem set and exit ticket.

What does the Fundamental Theorem of Similarity (FTS) imply about the dilation of a line?

• It becomes a perpendicular line.

• It remains unchanged.

• It becomes a parallel line.

• It becomes a curved line.

Which of the following remains unchanged during a dilation?

• The scale factor

• The size of the figure

• The shape of the figure

• The angle measures

What are the two key components needed to perform a dilation?

• Degrees and a center

• A line of reflection and a center

• A scale factor and a center

• A vector and a center

How is the dilation of a figure calculated using the dilation equation?

• Original figure divided by scale factor

• Original figure plus scale factor

• Original figure times scale factor

• Original figure minus scale factor

In the exercise, if PQ is 5 cm and P'Q' is 10 cm, what is the scale factor?

• 2

• 1

• 5

• 0.5

When verifying the scale factor, what should OP' equal if OP is 2.3 cm and the scale factor is 2?

• 2.3 cm

• 4.6 cm

• 5.6 cm

• 6.6 cm

What is the recommended method for finding a dilated point on a graph?

• Using the legs of a triangle

• Using the hypotenuse

• Using the diagonal

• Using the perimeter

If a point A is located at (3, 4) and the scale factor is 5/3, what is the new x-coordinate of A'?

• 4

• 5

• 3

• 5/3

Why is it often easier to use the legs of a triangle rather than the diagonal when calculating dilations on a graph?

• The legs are always equal.

• The legs are shorter.

• The legs provide simpler calculations.

• The diagonal is not visible.

What should you do if you need help understanding the problem set?

• Skip the problem set.

• Ignore the problem set.

• Ask the teacher for help.

• Use the diagonal for calculations.