Question

quiz 1
google classroom microsoft teams
complete the similarity statement.
a line segment is sometimes/always/never similar to another line
segment, because we can sometimes/always/never map one onto
the other using only dilations and rigid transformations.

Explanation:

Step1: Understand similarity of line segments

Two line segments are similar if their corresponding angles are equal (which they always are as all angles of line segments are \(0^{\circ}\) or \(180^{\circ}\)) and their side - length ratios are equal.

Step2: Consider rigid transformations and dilations

A rigid transformation (translation, rotation, reflection) preserves the shape and size of a figure. A dilation changes the size of a figure but not its shape.
For any two line segments \(AB\) and \(CD\), we can use a translation (to move one segment to the position of the other), and then a dilation. Let the length of segment \(AB = l_1\) and the length of segment \(CD=l_2\). The scale factor of the dilation \(k=\frac{l_2}{l_1}\) (if \(l_1
eq0\)).

Answer:

A line segment is always similar to another line segment, because we can always map one onto the other using only dilations and rigid transformations.