Two figures are similar if one can be mapped onto the other using a sequence of transformations consisting of translations, rotations, reflections, and dilations. Similar figures have the same shape, but they may have different sizes. However, not all rectangles have the same shape. Let's consider two example rectangles.
We know that when two figures are similar, the corresponding angles are congruent and the ratios of the lengths of corresponding sides are proportional. In our example, we know that every angle of one rectangle is congruent to every angle of the other rectangle since every angle in a rectangle is a right angle.
If the ratios of the lengths of corresponding sides of the two rectangles are not proportional, then the rectangles are not similar. Let's label the lengths of the sides of our rectangles.
If the two rectangles are similar, then the longer sides must be corresponding. Likewise, the shorter sides must be corresponding. Let's see if the ratios of the lengths of shorter and longer sides are proportional.
1/2 ≠2/3 *
The ratios of the measures of corresponding sides are not proportional, so the rectangles are not similar. Therefore, the given statement is false.
