Question

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: Recall the definition of similar figures

Similar figures have the same shape. All line segments have the same shape (they are one - dimensional straight paths).

Step2: Recall the properties of dilations and rigid transformations

A rigid transformation (translation, rotation, reflection) preserves the shape and size. A dilation changes the size but not the shape. For any two line segments, we can first use a rigid transformation to align them (if not already aligned) and then use a dilation. If the length of the first line segment is \(l_1\) and the length of the second is \(l_2\), 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.