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