Given: Trapezoid ABCD with median EF Prove: EF || AB || DC and EF = 0.5 (DC + AB) Statements Proof 1. Trapezoid ABCD with median EF. 1. Given 2. 2. The line postulate at G 3. AB || CD 3. 4. 4. Definition of median of trapezoid 5. ∠ABF ≅ ∠GCE 5. 6.∠BFA ≅ ∠CFG 6. 7. 7. ASA Postulate 8. 8. The midline of a triangle is parallel to the third side and is half as long. 9. EF || AB 9. 10. DG = DC + GC 10. 11. DG = DC + AB 11. 12. 12. Law of Substitution
Given: Trapezoid ABCD with median EF Prove: EF || AB || DC and EF = 0.5 (DC + AB) Statements Proof 1. Trapezoid ABCD with median EF. 1. Given 2. 2. The line postulate at G 3. AB || CD 3. 4. 4. Definition of median of trapezoid 5. ∠ABF ≅ ∠GCE 5. 6.∠BFA ≅ ∠CFG 6. 7. 7. ASA Postulate 8. 8. The midline of a triangle is parallel to the third side and is half as long. 9. EF || AB 9. 10. DG = DC + GC 10. 11. DG = DC + AB 11. 12. 12. Law of Substitution
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.2: Addition On A Number Line
Problem 35WE
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Question
Given: Trapezoid ABCD with median EF
Prove: EF || AB || DC and EF = 0.5 (DC + AB)
Statements |
Proof |
1. Trapezoid ABCD with median EF. |
1. Given |
2. |
2. The line postulate at G |
3. AB || CD |
3. |
4. |
4. Definition of median of trapezoid |
5. ∠ABF ≅ ∠GCE |
5. |
6.∠BFA ≅ ∠CFG |
6. |
7. |
7. ASA Postulate |
8. |
8. The midline of a |
9. EF || AB |
9. |
10. DG = DC + GC |
10. |
11. DG = DC + AB |
11. |
12. |
12. Law of Substitution |
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