Final answer:
In similar triangles, the ratio of the perimeters is equal to the ratio of their corresponding sides because the sides are proportional.
Step-by-step explanation:
In similar triangles, the ratio of the perimeters is equal to the ratio of their corresponding sides. To illustrate this, consider two similar triangles where the lengths of the sides of the first triangle are a, b, and c, and the lengths of the sides of the second triangle are ka, kb, and kc, where k is a positive constant.
Since the triangles are similar by definition, the corresponding angles are equal, and the ratios of the corresponding sides are in proportion. Therefore, the perimeter of the first triangle is a+b+c, and the perimeter of the second triangle is ka+kb+kc = k(a+b+c). Thus, the ratio of the perimeters of two similar triangles is equal to the ratio of any pair of corresponding sides, which is k in this case.