Properties of Scaled Copies
Properties of Scaled Copies is a Grade 7 math skill in Illustrative Mathematics, Chapter 1: Scale Drawings. Students explore how scaled copies preserve angle measures and maintain proportional side lengths, and understand what changes (size) versus what stays the same (shape and angles).
Key Concepts
If one figure is a scaled copy of another, two key properties are always true: 1. All corresponding angles are congruent (have the same measure). 2. The ratio of any pair of corresponding side lengths is constant and equal to the scale factor.
Common Questions
What properties are preserved in a scaled copy?
Scaled copies preserve all angle measures. All corresponding side lengths are in the same ratio (the scale factor). The shape is identical to the original.
What changes in a scaled copy?
The lengths of the sides change by the scale factor. The perimeter also scales by the same factor. The area changes by the square of the scale factor.
Are the angles in a scaled copy the same?
Yes. All corresponding angles in a scaled copy are exactly equal to the angles in the original figure.
What is a real-world example of using properties of scaled copies?
A map is a scaled copy of the actual geography. All angles (directions) are preserved, and distances scale by the map scale factor.
What chapter covers properties of scaled copies in Illustrative Mathematics Grade 7?
Properties of scaled copies are covered in Chapter 1: Scale Drawings in Illustrative Mathematics Grade 7.