Area is the number of square units that cover a two-dimensional region without gaps or overlaps.

• The area of region A is 8 square units.
• The area of the shaded region of B is \(\frac12\) square unit.

Corresponding parts are the parts that match up between a figure and its scaled copy. They have the same relative position. Points, segments, angles, or distances can be corresponding.

Point \(B\) in the first triangle corresponds to point \(E\) in the second triangle. Segment \(AC\) corresponds to segment \(DF\).

Two numbers that multiply to equal 1 are reciprocals.

• 8 and \(\frac{1}{8}\) are reciprocals because \(8 \boldcdot \frac{1}{8} = 1\).
• \(\frac{2}{5}\) is a reciprocal of \(\frac{5}{2}\) because \(\frac{2}{5} \boldcdot \frac{5}{2} = 1\).

A scale tells how the measurements in a scale drawing represent the actual measurements.

The scale on this floor plan tells us that 1 inch on the drawing represents 8 feet in the actual room. This means that 2 inches represent 16 feet, and \(\frac12\) inch represents 4 feet.

A scale drawing represents an actual place or object. All the measurements in the drawing correspond to the measurements of the actual object by the same scale.

To create a scaled copy of a figure, all the side lengths in the original figure are multiplied by the same number. This number is called the scale factor.

In this example, the scale factor is 1.5, because \(4 \boldcdot (1.5) = 6\), \(5 \boldcdot (1.5)=7.5\), and \(6 \boldcdot (1.5)=9\).

A scaled copy is a copy of a figure where every side length in the original figure is multiplied by the same number.

Triangle \(DEF\) is a scaled copy of triangle \(ABC\). Each side length on triangle \(ABC\) is multiplied by 1.5 to get the corresponding side length on triangle \(DEF\).