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What is the missing reason in steps 7 and 8 of the proof? Given: ?ABC with AB = c, BC = a, AC = b Prove: = = Statement Reason 1

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What is the missing reason in steps 7 and 8 of the proof? Given: ?ABC with AB = c, BC = a, AC = b Prove: = = Statement Reason 1. Draw a line through B that is perpendicular to and label the point of intersection with as D. construction 2. In ?ABD, BD = c sin A definition of sine in right triangle 3. In ?CBD, BD = a sin C definition of sine in right triangle 4. c sin A = a sin C Substitution Property of Equality 5. = dividing throughout by sin A sin C 6. Draw a line through A that is perpendicular to and label the point of intersection with as E. construction 7. In ?BAE, AE = c sin B 8. In ?CAE, AE = b sin C 9. c sin B = b sin C Substitution Property of Equality 10. = dividing throughout by sin B sin C 11. = = Transitive Property of Equality