# Fundamental Theorem of Similarity (FTS)

Video solutions to help Grade 8 students learn the properties related to the Fundamental Theorem of Similarity (FTS).

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Lessons for Grade 8
Common Core For Grade 8
## New York State Common Core Math Module 3, Grade 8, Lesson 4

### Lesson 4 Outcome

• Students experimentally verify the properties related to the Fundamental Theorem of Similarity (FTS).

### Lesson 4 Summary

Theorem: Given a dilation with center 0 and scale factor r, then for any two points P and Q in the plane so that 0,
P, and Q are not collinear, the lines PQ and P'Q' are parallel, where P' = dilation(P) and Q' = dilation(Q), and
furthermore, |P'Q'| = r|PQ|.

### NYS Math Module 3 Grade 8 Lesson 4

Classwork

Discussion

Exercise

1. In the diagram below, points R and S have been dilated from center 0, by a scale factor of r = 3.

a. If the length of |OR| = 3 cm, what is the length of |OR'|

b. If the length of |OS| = 3.5 cm, what is the length of |OS'|

c. Connect the point R to the point S and the point R' to the point S'. What do you know about lines RS and R'S'?

d. What is the relationship between the length of RS and the length of R'S'?

e. Identify pairs of angles that are equal in measure. How do you know they are equal?

Problem Set Sample Solutions

Students verify that the Fundamental Theorem of Similarity holds true when the scale factor is 0 < r < 1.