SOLUTION: Fill in the blanks to complete the two-column proof in the image. Here is a link to the image: https://imgur.com/a/b37H0iw These are my answers: 2. [1] Segment Addition Postula

  

Statements                Reasons 
1. EG = FH                1. Given
2. EG = EF + FG           2. [1] SEGMENT ADDITION POSTULATE
3. FH = FG + GH           3. Segment Addition   
4. EF + FG = FG + GH      4. [2] ADDITION PROPERTY OF EQUALITY
5. EF = GH                5. Subtraction Property of Equality

Your reason for 4 is wrong.  

The left side of statement 4, EF + FG, is equal to EG (from statement 2).
The right side of statement 4, FG + GH, is equal to FH (from statement 3).
EG and FH are equal things (from statement 1).



So EF + FG and FG + GH, respectively, are equal to equal things EG and FH, respectively.

So the postulate to give for 4 is

magnitudes equal to equal magnitudes are equal to each other

Justification:

https://archive.org/stream/planegeometry00duregoog/planegeometry00duregoog_djvu.txt

https://books.google.com/books?id=-i4AAAAAYAAJ&pg=PA26&lpg=PA26&dq=%22magnitudes+equal+to+equal+magnitudes+are+equal+to+each+other%22&source=bl&ots=b9rctac0iC&sig=ACfU3U0rvS7BnM8FWVV7vgt7-BbN_0dFGw&hl=en&sa=X&ved=2ahUKEwion67hqpb0AhUMTDABHdXMC6UQ6AF6BAgDEAM#v=onepage&q=%22magnitudes%20equal%20to%20equal%20magnitudes%20are%20equal%20to%20each%20other%22&f=false



 

Edwin