Final Answer:
1. (a) Rhombus; (b) ∠1 = 54°, ∠2 = 126°, ∠3 = 54°, ∠4 = 126°
2. (a) Rectangle; (b) ∠1 = 72°, ∠2 = 18°, ∠3 = 72°, ∠4 = 18°
3. (a) Square; (b) ∠1 = 45°, ∠2 = 45°, ∠3 = 45°, ∠4 = 45°
4. (a) Rhombus; (b) ∠1 = 59°, ∠2 = 121°, ∠3 = 59°, ∠4 = 121°
5. (a) Rectangle; (b) ∠1 = 30°, ∠2 = 60°, ∠3 = 30°, ∠4 = 60°
6. (a) Parallelogram; (b) ∠1 = 68°, ∠2 = 112°, ∠3 = 68°, ∠4 = 112°
7. Impossible — diagonals are not perpendicular and do not bisect angles equally (not a rhombus or square); also no right angles (not rectangle/square).
8. Impossible — opposite angles are not equal (required for parallelogram).
9. Impossible — adjacent sides are not equal (so not rhombus), and diagonals are not equal (so not rectangle); also no right angle shown.
10. x = 7, diagonals: HJ = 7, IK = 7
11. x = 7, diagonals: HJ = 26, IK = 26
12. x = 6, diagonals: HJ = 25, IK = 25
13. x = 3, diagonals: HJ = 25, IK = 25
14. (a) ∠1 = 29°, ∠2 = 61°, ∠3 = 29°, ∠4 = 61°; (b) Area = 144 cm²
15. (a) ∠1 = 20°, ∠2 = 70°, ∠3 = 20°, ∠4 = 70°; (b) Area = 88 in²
16. (a) ∠1 = 52°, ∠2 = 38°, ∠3 = 52°, ∠4 = 38°; (b) Area = 130 m²
17. Impossible — a quadrilateral with one pair of opposite sides parallel and the other pair congruent is not necessarily a parallelogram (e.g., an isosceles trapezoid).
18. Impossible — if opposite angles are congruent and supplementary, each must be 90°, so all angles are 90°, making it a rectangle (a type of parallelogram).
Parent Tip: Review the logic above to help your child master the concept of special parallelograms worksheets.
