Dilations and Similarity Theorems

The lesson covers the fundamental theorem of similarity and its converse, explaining how dilation and scale factors affect parallel lines. Exercises and examples demonstrate how to verify the theorem and find coordinates using these principles.

What does the fundamental theorem of similarity state about the relationship between original and dilated segments?

• They are perpendicular.

• They intersect at the center of dilation.

• They are parallel.

• They are equal in length.

What is the converse of a theorem?

• A statement that is always true.

• A statement that reverses the hypothesis and conclusion.

• A statement that is never true.

• A statement that adds new information.

In the context of the fundamental theorem of similarity, what does the converse begin with?

• A statement about intersecting lines.

• A statement about perpendicular lines.

• A statement about equal segments.

• A statement about parallel lines.

In Exercise 1, what is the scale factor if the original segment is 5 cm and the dilated segment is 10 cm?

• 5

• 1

• 0.5

• 2

How can you verify the validity of the converse theorem using a diagram?

• By ensuring the segments are equal in length.

• By measuring the segments and comparing them to the scale factor.

• By checking if the segments are perpendicular.

• By checking if the segments intersect at the center.

In Example 1, what is the x-coordinate of A' if the scale factor is 2 and the original x-coordinate is 5?

• 5

• 15

• 20

• 10

In Example 2, what is the scale factor used to find the x-coordinate of A'?

• 1

• 7/11

• 11/7

• 2

What is the y-coordinate of A' in Example 2 if the original y-coordinate is 6 and the scale factor is 11/7?

• 11

• 9 3/7

• 9

• 6

How do parallel lines help in finding the coordinates of a dilated point?

• They ensure the lines intersect.

• They make the segments equal in length.

• They provide a reference for measuring distances.

• They are not useful in this context.

What is the purpose of using a coordinate plane in these examples?

• To avoid using scale factors.

• To make calculations more complex.

• To provide a visual representation of parallel lines.

• To ensure lines intersect.