This lesson introduces students to the idea of a scaled copy, which is a two-dimensional image that has been recreated at a certain scale factor. Students learn to distinguish scaled copies from those that are not—first informally, and later, with increasing precision. They may start by saying that scaled copies have the same shape as the original figure, or that they do not appear to be distorted in any way, though they may have a different size. Next, students notice that the lengths of segments in a scaled copy vary from the lengths in the original figure in a uniform way. For instance, if a segment in a scaled copy is half the length of its counterpart in the original, then all other segments in the copy are also half the length of their original counterparts. Students work toward articulating the characteristics of scaled copies quantitatively (for example, “all the segments are twice as long,” “all the lengths have shrunk by one third,” or “all the segments are one-fourth the size of the segments in the original”), articulating the relationships carefully (MP6) along the way.

The lesson is designed to be accessible to all students regardless of prior knowledge, and to encourage students to make sense of problems and persevere in solving them (MP1) from the very beginning of the course.

If not mentioned by students before the Synthesis of Activity 2, ask how the idea of congruence is related to the idea of scaled copies. Students may bring up corresponding parts or recall how two triangles can have the same three angles but three different side lengths. It is not necessary to bring up these ideas if students do not. In later lessons, students will learn to describe this type of relationship between scaled copies using the language of transformations and dilations. For this lesson, student focus is on understanding what a scaled copy is and is not.