# Lesson 4

Scaled Relationships

### Lesson Narrative

In previous lessons, students looked at the relationship between a figure and a scaled copy by finding the scale factor that relates the side lengths and by using tracing paper to compare the angles. This lesson takes both of these comparisons a step further.

• Students study corresponding distances between points that are not connected by segments, in both scaled and unscaled copies. They notice that when a figure is a scaled copy of another, corresponding distances that are not connected by a segment are also related by the same scale factor as corresponding sides.
• Students 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.

Students use both insights—about angles and distances between points—to make a case for whether a figure is or is not a scaled copy of another (MP3). Practice with the use of protractors will help develop a sense for measurement accuracy, and how to draw conclusions from said measurements, when determining whether or not two angles are the same.

### Learning Goals

Teacher Facing

• Explain (orally and in writing) that corresponding angles in a figure and its scaled copies have the same measure.
• Identify (orally and in writing) corresponding distances or angles that can show that a figure is not a scaled copy of another.
• Recognize that corresponding distances in a figure and its scaled copy are related by the same scale factor as corresponding sides.

### Student Facing

Let’s find relationships between scaled copies.

### Required Preparation

Make sure students have access to their geometry toolkits, especially rulers and protractors.

### Student Facing

• I can use corresponding distances and corresponding angles to tell whether one figure is a scaled copy of another.
• When I see a figure and its scaled copy, I can explain what is true about corresponding angles.
• When I see a figure and its scaled copy, I can explain what is true about corresponding distances.