Technical Mathematics, Sixth Edition

17.2. Similar Figures

Our main use for ratio and proportion will be for similar figures, with applications to scale drawings, maps, and scale models.

▪ Exploration:

Try this.

1. Arrange four equal cardboard squares to form a square whose side is twice the side of a single square, Fig. 17-12(a). Measure the diagonal of a single square and also that of the four-square array. How do they compare? How does the area of the four-square array compare with the area of a single square?

2. Arrange eight children's blocks to form a cube, Fig. 17-12(b), each side of which is twice that of a single block. How does the volume of the eight-block cube compare with the volume of a single block?

Figure 17.12. FIGURE 17-12

Now suppose you had a scale drawing of a computer on which all dimensions were half those on the actual object, and the area of the screen measures 42 in.² on the drawing. What would you suppose the actual screen area would be?

Again given the half-scale drawing just mentioned, and the volume of the computer's case that measures 288 in.³ on the drawing, what would you suppose its actual volume would be?

We considered similar triangles in our chapter on geometry and said that corresponding sides were in proportion. We now expand the idea to cover similar plane figures of any shape, and also similar solids.

Similar figures (plane or solid) are those in which the distance between any two ...