Question

complete the two - column proof using the selections given. write the letter next to the number it corresponds with. given: ( ac = ab + ab ) prove: ( ab = bc )
diagram: a---b---c

statements	reasons
2. ( ab + bc = ac )	2.
3. ( ab + ab = ab + bc )	3. transitive property of equality
4. ( ab = bc )	4.

options:
a. symmetric property of equality
b. subtraction property of equality
c. segment addition postulate
d. addition property of equality

Explanation:

Step1: Analyze Reason for Statement 2

Statement 2 is \(AB + BC = AC\). The Segment Addition Postulate states that if a point \(B\) is between \(A\) and \(C\), then \(AB + BC = AC\). So the reason for statement 2 is the Segment Addition Postulate, which is option C.

Step2: Analyze Reason for Statement 4

Statement 3 is \(AB + AB = AB + BC\) and statement 4 is \(AB = BC\). To get from \(AB + AB = AB + BC\) to \(AB = BC\), we subtract \(AB\) from both sides, which is the Subtraction Property of Equality. So the reason for statement 4 is the Subtraction Property of Equality, which is option B.

Answer:

1. C (Segment Addition Postulate)
2. B (Subtraction Property of Equality)