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Step-by-step explanation:

The problem with  this kind o f question is that I likely can prove it, but I may not use the vocabulary that you do.

1 AC = BD             Given

2 AC = AB + BC             The sum of any two segments of a given line with is equal to another given line are equal. Put another way the sum of 2 parts of an equal line = the sum of any 2 parts of another equal line are equal. The sums are what is equal.

2a BD = BC + CD           Same reason as above.

3 AB + BC = BC + CD    The Since AC = BD then The sums on the the right making up AC and BD are equal.

4 AB = CD                      What I used to call the reflexive property. It means a segment appearing on both sides of an equal side can be subtracted out. A line segment is always equal to itself and can be subtracted out without loss of equality.

1. AC = BD                      1. Given

2. AC = AB + BC            2. Segment Addition Postulate

   BD = BC + CD

3. AB + BC = BC + CD     3. Substitution Property (refer to #s 1 & 2)

4. AB = CD                       4. Subtraction Property of Equality (subtracted BC)

step-by-step explan mxfcg'k; uafwgzfgjhklhgation: