In this lesson, students examine corresponding parts more closely, to make a case for whether a figure is or is not a scaled copy of another (MP3).

• Previously students saw that a scale factor relates the corresponding side lengths of a figure and a scaled copy. In this lesson, they notice that corresponding distances not connected by a segment are also related by the same scale factor as corresponding sides.
• Previously students used tracing paper to compare corresponding angles. In this lesson, they use protractors to test their observations about corresponding angles. They verify, in several sets of examples, that corresponding angles in a figure and its scaled copies are the same size.

Practice with the use of protractors helps develop a sense for measurement accuracy and for drawing conclusions from said measurements, such as determining whether or not two angles are the same.

Students also deepen their understanding of scale factors in two ways:

• They classify scale factors by size (less than 1, exactly 1, and greater than 1) and notice how each class of factors affects the scaled copies (MP8).
• They see that the scale factor that takes an original figure to its copy and the one that takes the copy to the original are reciprocals (MP7). This means that the scaling process is reversible, and that if Figure B is a scaled copy of Figure A, then Figure A is also a scaled copy of Figure B.

In the optional activity “Scaling a Puzzle,” students scale the 6 pieces of a puzzle individually and then assemble them to make a scaled copy of the puzzle. Students need to think strategically about which measurements to take in order to scale the pieces accurately.