Question

select the correct answer from each drop - down menu.
given: ( u x = w z quad v w = x y )
prove: ( u v = y z )

statements	reasons
2. ( \begin{array} { r l } { u x } & { = u v + v w + w x } \\ { w z } & { = w x + x y + y z } end{array} )	2. segment addition
3. ( u v + v w + w x = w x + x y + y z )	3. addition property of equality
4. ( u v + v w = x y + y z )	4. subtraction property of equality
5. ( v w = x y )	5. given
6. ( u v = y z )	6. subtraction property of equality

where is the first error in this proof?
the reason in line ( 3 ) does not justify the statement because
be ( ) the substitution property of equality ( ). instead, the reason should

Explanation:

Step1: Analyze the addition property of equality

The addition property of equality states that if \(a = b\), then \(a + c=b + c\). In line 3, we are substituting \(UX\) with \(UV + VW+WX\) and \(WZ\) with \(WX + XY + YZ\) (since \(UX = WZ\) from line 1). This is not an application of the addition property of equality.

Step2: Analyze the substitution property of equality

The substitution property of equality states that if \(a = b\), then \(a\) can be replaced by \(b\) in any equation. Here, since \(UX=UV + VW+WX\) (line 2), \(WZ = WX + XY + YZ\) (line 2) and \(UX = WZ\) (line 1), we substitute \(UX\) with \(UV + VW+WX\) and \(WZ\) with \(WX + XY + YZ\) in the equation \(UX = WZ\). So the correct property is substitution.

Answer:

values were not added to each side