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 = BDReason: Given

31. Statement: AC = AB + BCReason: Segment Addition Postulate

32. Statement: AB +BC = BDReason: Substitution Property of Equality

33. Statement: BD = BC + CDReason: Segment Addition Postulate

34. Statement: AB + BC = BC + CDReason: Substitution Property of Equality (Or is it the transitive property?)

35. Statement: AB= CDReason: Subtraction Property of Equality

36. Statement: CD = ABReason: Symmetric Property of Equality

37. Statement:Reason: Definition of congruent segments(line segment) CD ≅(line segment) AB

Any help you guys can give would be greatly appreciated!