1. The two triangles, ΔABC and ΔXYZ, are similar by the AA (Angle-Angle) similarity criterion because both are right triangles (angle C and angle Z are 90°) and their corresponding angles are equal.
2. Since the triangles are similar, the ratios of their corresponding sides are equal. The ratio of the hypotenuses is 17:25.5, which simplifies to 2:3.
3. Therefore, the ratio of any pair of corresponding sides is 2:3.
4. To find side 'a' (side CB), set up the proportion using the known corresponding sides: a / 12 = 17 / 25.5.
5. Solving for 'a': a = (17 * 12) / 25.5 = 204 / 25.5 = 8.
6. To find side 'y' (side XZ), set up the proportion: 15 / y = 17 / 25.5.
7. Solving for 'y': y = (15 * 25.5) / 17 = 382.5 / 17 = 22.5.
8. The values are a = 8 and y = 22.5.
Parent Tip: Review the logic above to help your child master the concept of proportions and similar triangles worksheet.
