Projecting and Scaling

Student Summary

In this diagram, the larger rectangle is a scaled copy of the smaller one, and the scale factor is 32\frac32 because 432=64 \boldcdot \frac32=6 and 232=32 \boldcdot \frac32=3. Scaled copies of rectangles have another interesting property: the diagonal of the large rectangle contains the diagonal of the smaller rectangle. This is the case for any two scaled copies of a rectangle if we line them up as shown. If two rectangles are not scaled copies of one another, then their diagonals would not match up.

Two rectangles with one dashed diagonal line through both.
A small rectangle inside a larger rectangle with same lower left point and a dashed diagonal line from that lower left point through both upper points. The small rectangle has length 4 and height 2. The large rectangle has length 6 and height 3.

Visual / Anchor Chart

Standards

Building On
6.NS.A

6.NS.A

7.G.1

7.G.A.1

7.G.1

7.G.A.1

Building Toward
8.G.A

8.G.A

8.G.A

8.G.A