Question

select the correct answer from each drop - down menu. given: (ux = wz), (vw = xy) prove: (uv = yz) (there is a number line with points u, v, w, x, y, z in order) (\begin{array}{|l|l|} hline \text{statements} & \text{reasons} \\ hline 1. ux = wz & 1. \text{given} \\ hline 2. \begin{aligned}ux&=uv + vw + wx\wz&=wx + xy + yzend{aligned} & 2. \text{segment addition} \\ hline 3. uv + vw + wx = wx + xy + yz & 3. \text{addition property of equality} \\ hline 4. uv + vw = xy + yz & 4. \text{subtraction property of equality} \\ hline 5. vw = xy & 5. \text{given} \\ hline 6. uv = yz & 6. \text{subtraction property of equality} \\ hline end{array}) where is the first error in this proof? the reason in line (\boldsymbol{3}) does not justify the statement because (\boldsymbol{\text{drop - down menu}}) instead, the reason should be (\boldsymbol{\text{the substitution property of equality}}) (the drop - down menu options include: more than two segments were added, values were not added to each side, values were not subtracted from each side)

Explanation:

1. First error location: Line 3 uses the "addition property of equality" incorrectly. This property requires adding the same value to both sides of an equation, but here we substituted \(UX = UV + VW + WX\) and \(WZ = WX + XY + YZ\) into \(UX=WZ\).
2. Reason for error: The addition property was misapplied because no values were added to each side of the original equation.
3. Correct reason: The substitution property of equality (replacing equal quantities with their equivalents) is the proper justification for this step.

Answer:

The first error is in line 3.

• The reason in line 3 does not justify the statement because values were not added to each side.
• Instead, the reason should be the substitution property of equality.