Final answer:
The ratios of corresponding sides in ΔABC and ΔADE would be equal, indicative of similar triangles with sides that are proportional. For example, if the sides of one triangle are twice as long as the corresponding sides of another, the ratio would be 1:2. Areas of similar squares compare by the square of the ratio of their side lengths.
Step-by-step explanation:
When observing the ratios of corresponding sides in ΔABC and ΔADE, one would notice that despite the differences in sizes of the two triangles, these ratios are equal. This is evidence of similar triangles, where triangles have the same shape but different sizes, and their corresponding sides are proportional. This concept is a key principle in geometry, often used to solve problems about scaling and comparing different shapes. To illustrate this with an example, if ΔABC and ΔADE are similar, and the sides of ΔABC are respectively 2, 3, and 4 units long, and the sides of ΔADE are 4, 6, and 8 units long, the ratio for each corresponding pair of sides (AB/AD, BC/AE, AC/DE) would be 1:2. As for the comparison of areas, if the sides of a square are doubled, the area is quadrupled (since area is proportional to the square of the side length), so the ratio of the areas of two similar squares would be the square of the ratio of their side lengths.