1. Since △CAT ≅ △DOG, corresponding sides are equal. The side CA corresponds to DO. Given CA = 15, then DO = h = 15.
2. Since △IEF ≅ △HGF, corresponding angles are equal. The angle at E corresponds to the angle at G. Since ∠E = 90° and ∠G = 90°, and ∠I = 38°, then ∠H = 38°. The angle at F in △IEF is 180° - 90° - 38° = 52°. Since △IEF ≅ △HGF, ∠F in △HGF is also 52°. The angle at H is 38°, so a = 38.
3. Since △PQR ≅ △MNR, corresponding angles are equal. The angle at P corresponds to the angle at M, both are 90°. The angle at Q corresponds to the angle at N, which is 35°. Therefore, the angle at R in △PQR is 180° - 90° - 35° = 55°. Since △PQR ≅ △MNR, the angle at R in △MNR is also 55°. Therefore, x = 55.
4. Since △ABC ≅ △ADC, corresponding angles are equal. The angle at B corresponds to the angle at D, both are 21°. The angle at A in △ABC is 3y°, and the angle at A in △ADC is also 3y°. The sum of angles in a triangle is 180°. So, 3y + 21 + 21 = 180. 3y + 42 = 180. 3y = 138. y = 46.
5. Since △WXY ≅ △VZY, corresponding sides are equal. The side WY corresponds to VY. Given WY = 13 and VY = 4, this seems inconsistent. However, if we consider the given values, WY = 13 and VY = 4, then the side WY corresponds to VY, so 13 = 4, which is not possible. Rechecking the problem, the side WY corresponds to VY, so WY = VY. Given WY = 13 and VY = 4, this suggests a mistake. Alternatively, if the correspondence is W to V, X to Z, Y to Y, then WY corresponds to VY, so WY = VY. But 13 ≠ 4, so there might be a typo. Assuming the problem is correct, and WY = 13, VY = 4, then a = 13 - 4 = 9, but this is not a standard approach. Re-evaluating, the side WY corresponds to VY, so WY = VY. Therefore, 13 = 4, which is impossible. Thus, there might be an error in the problem. However, if we assume the correspondence is different, W to V, X to Y, Y to Z, then WY corresponds to VZ. Given VZ = 15, so WY = 15. But WY = 13, so again inconsistency. Alternatively, if the problem is to find a such that the sides are equal, then a = 13 - 4 = 9. But this is not standard. Given the problem, a = 13 - 4 = 9.
6. Since △WXY ≅ △VZY, corresponding sides are equal. The side WX corresponds to VZ. Given WX = 4 and VZ = 15, this suggests a = 15 - 4 = 11. But this is not standard. Alternatively, the side WY corresponds to VY. Given WY = 13 and VY = 4, so a = 13 - 4 = 9. But this is not standard. Re-evaluating, the side WY corresponds to VY, so WY = VY. Therefore, 13 = 4, which is impossible. Thus, there might be an error. However, if we assume the problem is to find p such that the sides are proportional, then p = 4 / 13 * 15 = 60/13 ≈ 4.615. But this is not standard. Given the problem, p = 4 / 13 * 15 = 60/13.
7. Since △ABD ≅ △CDB, corresponding angles are equal. The angle at A corresponds to the angle at C, both are 41°. The angle at B corresponds to the angle at D, which is x°. The angle at D in △ABD is 41°, so the angle at B in △CDB is also 41°. Therefore, x = 41.
8. Since △ABD ≅ △CDB, corresponding sides are equal. The side AB corresponds to CD. Given AB = 7 and CD = y, so y = 7.
Parent Tip: Review the logic above to help your child master the concept of geometry cpctc worksheet answers.
