Hello everybody! This is a question from my sister's geometry book. I have crudely recreated the image from the book below. We are given statements, we're supposed to supply the reasons. Text as written in the book will be bold, my answers will be in blue.
Given: AC = BD
Prove: (line segment) CD ≅ (line segment) AB
30. Statement: AC = BD Reason: Given
31. Statement: AC = AB + BC Reason: Segment Addition Postulate
32. Statement: AB +BC = BD Reason: Substitution Property of Equality
33. Statement: BD = BC + CD Reason: Segment Addition Postulate
34. Statement: AB + BC = BC + CD Reason: Substitution Property of Equality (Or is it the transitive property?)
35. Statement: AB = CD Reason: Subtraction Property of Equality
36. Statement: CD = AB Reason: Symmetric Property of Equality
37. Statement: (line segment) CD ≅ (line segment) AB Reason: Definition of congruent segments
Any help you guys can give would be greatly appreciated!