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Step-by-step solution for: Parallelograms-1 - Geometry Name: Date: Parallelogram Worksheet I ...
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Show Answer Key & Explanations
Step-by-step solution for: Parallelograms-1 - Geometry Name: Date: Parallelogram Worksheet I ...
Since the options provided are all false (ExplainAnswer: false, TeachTopic: false, GeneratePractice: false), we will proceed directly to solving the problem and providing the final answer.
#### Section I: Complete each statement.
1. Opposite sides of a parallelogram are:
- Parallel and Congruent
2. In a parallelogram, consecutive angles are:
- Supplementary
3. The diagonals of a parallelogram:
- Bisect each other
4. If one angle of a parallelogram is a right angle, then it is a:
- Rectangle
#### Section II: Complete each statement, using Parallelogram ABCD.
5. If \( AB = 12 \) cm, then \( CD = \) cm:
- Since opposite sides of a parallelogram are congruent, \( CD = 12 \) cm.
6. If \( AD = 15 \) cm, then \( BC = \) cm:
- Since opposite sides of a parallelogram are congruent, \( BC = 15 \) cm.
7. If \( \angle A = 70^\circ \), then \( \angle C = \) degrees:
- Opposite angles of a parallelogram are congruent, so \( \angle C = 70^\circ \).
8. If \( \angle B = 110^\circ \), then \( \angle D = \) degrees:
- Opposite angles of a parallelogram are congruent, so \( \angle D = 110^\circ \).
9. If \( \angle A = 70^\circ \), then \( \angle B = \) degrees:
- Consecutive angles of a parallelogram are supplementary, so \( \angle B = 180^\circ - 70^\circ = 110^\circ \).
10. If \( AC = 20 \) cm and \( BD = 18 \) cm, then \( AE = \) cm:
- The diagonals of a parallelogram bisect each other, so \( AE = \frac{AC}{2} = \frac{20}{2} = 10 \) cm.
11. If \( AC = 20 \) cm and \( BD = 18 \) cm, then \( BE = \) cm:
- The diagonals of a parallelogram bisect each other, so \( BE = \frac{BD}{2} = \frac{18}{2} = 9 \) cm.
12. If \( AC = 20 \) cm and \( BD = 18 \) cm, then \( CE = \) cm:
- The diagonals of a parallelogram bisect each other, so \( CE = \frac{AC}{2} = \frac{20}{2} = 10 \) cm.
13. If \( AC = 20 \) cm and \( BD = 18 \) cm, then \( DE = \) cm:
- The diagonals of a parallelogram bisect each other, so \( DE = \frac{BD}{2} = \frac{18}{2} = 9 \) cm.
#### Section III: Find the missing measurements of Parallelogram ABCD.
Given:
- \( AB = 10 \) cm
- \( BC = 15 \) cm
- \( \angle A = 70^\circ \)
- \( \angle B = 110^\circ \)
- \( AC = 20 \) cm
- \( BD = 18 \) cm
14. \( CD = \) cm:
- Opposite sides of a parallelogram are congruent, so \( CD = AB = 10 \) cm.
15. \( AD = \) cm:
- Opposite sides of a parallelogram are congruent, so \( AD = BC = 15 \) cm.
16. \( \angle C = \) degrees:
- Opposite angles of a parallelogram are congruent, so \( \angle C = \angle A = 70^\circ \).
17. \( \angle D = \) degrees:
- Opposite angles of a parallelogram are congruent, so \( \angle D = \angle B = 110^\circ \).
18. \( AE = \) cm:
- The diagonals of a parallelogram bisect each other, so \( AE = \frac{AC}{2} = \frac{20}{2} = 10 \) cm.
19. \( BE = \) cm:
- The diagonals of a parallelogram bisect each other, so \( BE = \frac{BD}{2} = \frac{18}{2} = 9 \) cm.
20. \( CE = \) cm:
- The diagonals of a parallelogram bisect each other, so \( CE = \frac{AC}{2} = \frac{20}{2} = 10 \) cm.
21. \( DE = \) cm:
- The diagonals of a parallelogram bisect each other, so \( DE = \frac{BD}{2} = \frac{18}{2} = 9 \) cm.
1. Opposite sides of a parallelogram are:
- Parallel and Congruent
2. In a parallelogram, consecutive angles are:
- Supplementary
3. The diagonals of a parallelogram:
- Bisect each other
4. If one angle of a parallelogram is a right angle, then it is a:
- Rectangle
5. If \( AB = 12 \) cm, then \( CD = \) cm:
- 12 cm
6. If \( AD = 15 \) cm, then \( BC = \) cm:
- 15 cm
7. If \( \angle A = 70^\circ \), then \( \angle C = \) degrees:
- 70 degrees
8. If \( \angle B = 110^\circ \), then \( \angle D = \) degrees:
- 110 degrees
9. If \( \angle A = 70^\circ \), then \( \angle B = \) degrees:
- 110 degrees
10. If \( AC = 20 \) cm and \( BD = 18 \) cm, then \( AE = \) cm:
- 10 cm
11. If \( AC = 20 \) cm and \( BD = 18 \) cm, then \( BE = \) cm:
- 9 cm
12. If \( AC = 20 \) cm and \( BD = 18 \) cm, then \( CE = \) cm:
- 10 cm
13. If \( AC = 20 \) cm and \( BD = 18 \) cm, then \( DE = \) cm:
- 9 cm
14. \( CD = \) cm:
- 10 cm
15. \( AD = \) cm:
- 15 cm
16. \( \angle C = \) degrees:
- 70 degrees
17. \( \angle D = \) degrees:
- 110 degrees
18. \( AE = \) cm:
- 10 cm
19. \( BE = \) cm:
- 9 cm
20. \( CE = \) cm:
- 10 cm
21. \( DE = \) cm:
- 9 cm
Step-by-Step Solution
#### Section I: Complete each statement.
1. Opposite sides of a parallelogram are:
- Parallel and Congruent
2. In a parallelogram, consecutive angles are:
- Supplementary
3. The diagonals of a parallelogram:
- Bisect each other
4. If one angle of a parallelogram is a right angle, then it is a:
- Rectangle
#### Section II: Complete each statement, using Parallelogram ABCD.
5. If \( AB = 12 \) cm, then \( CD = \) cm:
- Since opposite sides of a parallelogram are congruent, \( CD = 12 \) cm.
6. If \( AD = 15 \) cm, then \( BC = \) cm:
- Since opposite sides of a parallelogram are congruent, \( BC = 15 \) cm.
7. If \( \angle A = 70^\circ \), then \( \angle C = \) degrees:
- Opposite angles of a parallelogram are congruent, so \( \angle C = 70^\circ \).
8. If \( \angle B = 110^\circ \), then \( \angle D = \) degrees:
- Opposite angles of a parallelogram are congruent, so \( \angle D = 110^\circ \).
9. If \( \angle A = 70^\circ \), then \( \angle B = \) degrees:
- Consecutive angles of a parallelogram are supplementary, so \( \angle B = 180^\circ - 70^\circ = 110^\circ \).
10. If \( AC = 20 \) cm and \( BD = 18 \) cm, then \( AE = \) cm:
- The diagonals of a parallelogram bisect each other, so \( AE = \frac{AC}{2} = \frac{20}{2} = 10 \) cm.
11. If \( AC = 20 \) cm and \( BD = 18 \) cm, then \( BE = \) cm:
- The diagonals of a parallelogram bisect each other, so \( BE = \frac{BD}{2} = \frac{18}{2} = 9 \) cm.
12. If \( AC = 20 \) cm and \( BD = 18 \) cm, then \( CE = \) cm:
- The diagonals of a parallelogram bisect each other, so \( CE = \frac{AC}{2} = \frac{20}{2} = 10 \) cm.
13. If \( AC = 20 \) cm and \( BD = 18 \) cm, then \( DE = \) cm:
- The diagonals of a parallelogram bisect each other, so \( DE = \frac{BD}{2} = \frac{18}{2} = 9 \) cm.
#### Section III: Find the missing measurements of Parallelogram ABCD.
Given:
- \( AB = 10 \) cm
- \( BC = 15 \) cm
- \( \angle A = 70^\circ \)
- \( \angle B = 110^\circ \)
- \( AC = 20 \) cm
- \( BD = 18 \) cm
14. \( CD = \) cm:
- Opposite sides of a parallelogram are congruent, so \( CD = AB = 10 \) cm.
15. \( AD = \) cm:
- Opposite sides of a parallelogram are congruent, so \( AD = BC = 15 \) cm.
16. \( \angle C = \) degrees:
- Opposite angles of a parallelogram are congruent, so \( \angle C = \angle A = 70^\circ \).
17. \( \angle D = \) degrees:
- Opposite angles of a parallelogram are congruent, so \( \angle D = \angle B = 110^\circ \).
18. \( AE = \) cm:
- The diagonals of a parallelogram bisect each other, so \( AE = \frac{AC}{2} = \frac{20}{2} = 10 \) cm.
19. \( BE = \) cm:
- The diagonals of a parallelogram bisect each other, so \( BE = \frac{BD}{2} = \frac{18}{2} = 9 \) cm.
20. \( CE = \) cm:
- The diagonals of a parallelogram bisect each other, so \( CE = \frac{AC}{2} = \frac{20}{2} = 10 \) cm.
21. \( DE = \) cm:
- The diagonals of a parallelogram bisect each other, so \( DE = \frac{BD}{2} = \frac{18}{2} = 9 \) cm.
Final Answer
1. Opposite sides of a parallelogram are:
- Parallel and Congruent
2. In a parallelogram, consecutive angles are:
- Supplementary
3. The diagonals of a parallelogram:
- Bisect each other
4. If one angle of a parallelogram is a right angle, then it is a:
- Rectangle
5. If \( AB = 12 \) cm, then \( CD = \) cm:
- 12 cm
6. If \( AD = 15 \) cm, then \( BC = \) cm:
- 15 cm
7. If \( \angle A = 70^\circ \), then \( \angle C = \) degrees:
- 70 degrees
8. If \( \angle B = 110^\circ \), then \( \angle D = \) degrees:
- 110 degrees
9. If \( \angle A = 70^\circ \), then \( \angle B = \) degrees:
- 110 degrees
10. If \( AC = 20 \) cm and \( BD = 18 \) cm, then \( AE = \) cm:
- 10 cm
11. If \( AC = 20 \) cm and \( BD = 18 \) cm, then \( BE = \) cm:
- 9 cm
12. If \( AC = 20 \) cm and \( BD = 18 \) cm, then \( CE = \) cm:
- 10 cm
13. If \( AC = 20 \) cm and \( BD = 18 \) cm, then \( DE = \) cm:
- 9 cm
14. \( CD = \) cm:
- 10 cm
15. \( AD = \) cm:
- 15 cm
16. \( \angle C = \) degrees:
- 70 degrees
17. \( \angle D = \) degrees:
- 110 degrees
18. \( AE = \) cm:
- 10 cm
19. \( BE = \) cm:
- 9 cm
20. \( CE = \) cm:
- 10 cm
21. \( DE = \) cm:
- 9 cm
Parent Tip: Review the logic above to help your child master the concept of parallelogram worksheet geometry answers.
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