Theorem: If one pair of opposite sides of a quadrilateral are both parallel and congruent, the quadrilateral is a parallelogram. Given: Segment AB ≅ Segment CD, Segment AB||Segment CD Prove: ABCD is a parallelogram Complete the proof by writing the missing reasons. You may need to use some of the reasons more than once. Choose from the following reasons. Alternate Interior Angle Theorem CPCTC SAS Definition of Parallelogram Construction - Two points determine exactly one line. Definition of Alternate Interior Angles Converse of Alternate Interior Angle Theorem Given Statements Reasons Segment AB ≅ Segment CD 9. Segment AB||Segment CD 10. Draw a segment from A to C 11. Construction - Two points determine exactly one line. ∠ACD and ∠CAB are alternate interior angles 12. ∠ACD≅∠CAB 13. ΔABC≅ΔCDA 14. ∠CAD ≅∠ACB 15. Segment AD||Segment BC 16. ABCD is a parallelogram 17.
Theorem: If one pair of opposite sides of a quadrilateral are both parallel and congruent, the quadrilateral is a parallelogram. Given: Segment AB ≅ Segment CD, Segment AB||Segment CD Prove: ABCD is a parallelogram Complete the proof by writing the missing reasons. You may need to use some of the reasons more than once. Choose from the following reasons. Alternate Interior Angle Theorem CPCTC SAS Definition of Parallelogram Construction - Two points determine exactly one line. Definition of Alternate Interior Angles Converse of Alternate Interior Angle Theorem Given Statements Reasons Segment AB ≅ Segment CD 9. Segment AB||Segment CD 10. Draw a segment from A to C 11. Construction - Two points determine exactly one line. ∠ACD and ∠CAB are alternate interior angles 12. ∠ACD≅∠CAB 13. ΔABC≅ΔCDA 14. ∠CAD ≅∠ACB 15. Segment AD||Segment BC 16. ABCD is a parallelogram 17.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Theorem: If one pair of opposite sides of a quadrilateral are both parallel and congruent, the quadrilateral is a parallelogram.
Given: Segment AB ≅ Segment CD, Segment AB||Segment CD |
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|
Prove: ABCD is a parallelogram |
Complete the proof by writing the missing reasons. You may need to use some of the reasons more than once. Choose from the following reasons.
- Alternate Interior Angle Theorem
- CPCTC
- SAS
- Definition of Parallelogram
- Construction - Two points determine exactly one line.
- Definition of Alternate Interior
Angles - Converse of Alternate Interior Angle Theorem
- Given
|
Statements |
Reasons |
|
Segment AB ≅ Segment CD |
9. |
|
Segment AB||Segment CD |
10. |
|
Draw a segment from A to C |
11. Construction - Two points determine exactly one line. |
|
∠ACD and ∠CAB are alternate interior angles |
12. |
|
∠ACD≅∠CAB |
13. |
|
ΔABC≅ΔCDA |
14. |
|
∠CAD ≅∠ACB |
15. |
|
Segment AD||Segment BC |
16. |
|
ABCD is a parallelogram |
17. |
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