3. Justify each step in the following proof of Proposition I(SEGMENT SUBTRACTION). IFA' B *C.D'E'F. AB= DE, and ACDF, then BCEFI PROOF: (1) Assume on the contrary that BC is not congruent to EF. (2) Then there is a point G on Ef such that BC e EG. (3) G+ F. (4) Since AB DE, adding gives AC DG. (5) However, AC DF. (6) Hence, DF DG. (7) Therefore, F G. (8) Our assumption has led to a contradiction; hence, BC EF.

3. Justify each step in the following proof of Proposition I(SEGMENT SUBTRACTION). IFA' B *C.D'E'F. AB= DE, and ACDF, then BCEFI PROOF: (1) Assume on the contrary that BC is not congruent to EF. (2) Then there is a point G on Ef such that BC e EG. (3) G+ F. (4) Since AB DE, adding gives AC DG. (5) However, AC DF. (6) Hence, DF DG. (7) Therefore, F G. (8) Our assumption has led to a contradiction; hence, BC EF.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter1: Line And Angle Relationships

Section1.4: Relationships: Perpendicular Lines

Problem 12E: In Exercise 11 and 12, provide the missing statements and reasons. Given: 12;34 s 2 and 3 are...

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