Question

proof complete the two - column proof by dragging the missing statements and reasons into the correct order. given: b is the midpoint of $overline{ac}$. prove: $x = 17$. statements: 1. b is the midpoint of $overline{ac}$. 2.? 3. $3x + 3=x + 37$. 4.? 5.? 6. $2x=34$. 7.? reasons: 1.? 2. midpoint theorem. 3. definition of congruent segments. 4.? 5. subtraction property of equality. 6.? 7. division property of equality.

Explanation:

Step1: Apply mid - point theorem

Since B is the mid - point of $\overline{AC}$, by the mid - point theorem, $AB = BC$. So, $3x + 3=x + 37$.

Step2: Use subtraction property of equality

Subtract $x$ from both sides: $(3x + 3)-x=(x + 37)-x$. This simplifies to $2x+3 = 37$.

Step3: Use subtraction property of equality again

Subtract 3 from both sides: $(2x + 3)-3=37 - 3$. We get $2x=34$.

Step4: Use division property of equality

Divide both sides by 2: $\frac{2x}{2}=\frac{34}{2}$. So, $x = 17$.

Answer:

1. Given: B is the mid - point of $\overline{AC}$
2. Midpoint Theorem: $AB = BC$, so $3x + 3=x + 37$
3. Subtraction Property of Equality: $(3x + 3)-x=(x + 37)-x$, $2x+3 = 37$
4. Subtraction Property of Equality: $(2x + 3)-3=37 - 3$, $2x=34$
5. Division Property of Equality: $\frac{2x}{2}=\frac{34}{2}$, $x = 17$