Given: Trapezoid ABCD with median EFProve: EF || AB || DC and EF = 0.5 (DC + AB)StatementsProof1. Trapezoid ABCD with median EF.1. Given2. 2. The line postulate at G3. AB || CD3.4.4. Definition of median of trapezoid5. ∠ABF ≅ ∠GCE5.6.∠BFA ≅ ∠CFG6.7.7. ASA Postulate8.8. The midline of a triangle is parallel to the third side and is half as long.9. EF || AB9.10. DG = DC + GC10.11. DG = DC + AB11.12.12. Law of Substitution BAF

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Answered: Given: Trapezoid ABCD with median EF…

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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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

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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