Fundamental Theorem of Similarity Concepts

This video tutorial covers lesson 5 of module 3, focusing on dilations and the fundamental theorem of similarity (FTS). It explains the theorem, its converse, and provides examples and exercises to illustrate these concepts. The lesson emphasizes understanding the properties of dilations, parallel segments, and scale factors, and how to apply the theorem and its converse in various geometric contexts.

What is a surprising result of the Fundamental Theorem of Similarity when dilating segments?

• The segments become perpendicular.

• The segments remain unchanged.

• The segments become parallel and proportional.

• The segments disappear.

What does the converse of the Fundamental Theorem of Similarity state?

• If two segments are perpendicular, they are related by a scale factor.

• If two segments are parallel and related by a scale factor, there is a dilation.

• If two segments are parallel, they are equal in length.

• If two segments are parallel, they are not related by a scale factor.

Which of the following is an example of a true converse statement?

• If the water is running, then the faucet is on.

• If the faucet is on, then the water is running.

• If the ground is wet, then it is raining.

• If it is raining, then the ground is wet.

How can you find the center of dilation for two dilated segments?

• By measuring the angles between the segments.

• By drawing lines through the original and dilated points and finding their intersection.

• By finding the midpoint of the segments.

• By calculating the area of the segments.

What is the scale factor if the original segment is 4.3 cm and the dilated segment is 8.6 cm?

• 3

• 4

• 1

• 2

In a dilation with a scale factor of 2, what happens to the length of a segment?

• It remains the same.

• It is doubled.

• It is tripled.

• It is halved.

What is the x-coordinate of a point A' if point A is at (5, 2) and the scale factor is 2?

• 5

• 10

• 15

• 20

If a point A is at (3, 3) and is dilated by a scale factor of 4, what are the coordinates of A'?

• (6, 6)

• (12, 12)

• (3, 3)

• (9, 9)

What is the y-coordinate of a point A' if point A is at (7, 6) and the scale factor is 11/7?

• 7

• 11

• 6

• 9.4

In a dilation with a scale factor of 5/8, what happens to the length of a segment?

• It is reduced to 5/8 of its original length.

• It remains the same.

• It is increased to 8/5 of its original length.

• It is doubled.