Final answer:
To calculate corresponding sides and hypotenuses of similar triangles, use side length ratios and the Pythagorean theorem. The hypotenuse is found with c = √(a² + b²). Confirm the similarity through the proportion of corresponding sides, and map one triangle onto the other via transformations.
Step-by-step explanation:
When looking at similar triangles and calculating corresponding sides, you can use the ratios of the sides to determine the lengths. Using the Pythagorean theorem, which is c = √(a² + b²), we can calculate the hypotenuse of each triangle given the lengths of the other two sides.
For a triangle with side lengths of 15 and 8, the hypotenuse would be c = √(15² + 8²) = √(225 + 64) = √289 = 17. For a triangle with side lengths of 20 and a corresponding side length (b) that is similar to the side length of 8 in the first triangle, you can find the length of b using a proportion. If the triangles are similar, the ratio would hold true: 8/15 = b/20, thus b = (8 * 20)/15.
Calculating the length of the hypotenuse of the second triangle with the found value of b will tell us if the ratio of the hypotenuses is equal to the ratios of the corresponding sides. The sequence of transformations that would map one triangle onto the other can include scaling (dilation), rotation, and translation, assuming the triangles are similar in shape but different in size.