Question

10/1/28, 8:46 am wellington francis
question 1
a two - column proof has been partially completed, as shown.
statement reason

1. $overline{ac}=2overline{ab}$ 1. given
2. $overline{ac}=overline{ab}+overline{bc}$ 2.
3. $2overline{ab}=overline{ab}+overline{bc}$ 3.
4. $overline{ab}=overline{bc}$ 4.

Explanation:

Step1: Recall segment - addition postulate

The segment - addition postulate states that if B is between A and C, then $\overline{AC}=\overline{AB}+\overline{BC}$. So the reason for statement 2 is the Segment - Addition Postulate.

Step2: Substitute

Since $\overline{AC} = 2\overline{AB}$ (from statement 1) and $\overline{AC}=\overline{AB}+\overline{BC}$ (from statement 2), we can substitute $\overline{AC}$ in the second equation with $2\overline{AB}$ from the first equation. So the reason for statement 3 is Substitution Property of Equality.

Step3: Solve for $\overline{AB}$ and $\overline{BC}$

Starting with $2\overline{AB}=\overline{AB}+\overline{BC}$, we subtract $\overline{AB}$ from both sides of the equation. By the Subtraction Property of Equality, $2\overline{AB}-\overline{AB}=\overline{AB}+\overline{BC}-\overline{AB}$, which simplifies to $\overline{AB}=\overline{BC}$. So the reason for statement 4 is Subtraction Property of Equality.

Answer:

1. Segment - Addition Postulate
2. Substitution Property of Equality
3. Subtraction Property of Equality