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}{l}u x=u v+v w+w x \\ w z=w x+x y+y zend{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 ( square ) does not justify the statement because ( square ). instead, the reason should be ( square ).

Explanation:

Step1: Analyze line 3

Line 3 uses the addition property of equality. But since \(UX = WZ\) (from line 1) and \(UX=UV + VW+WX\), \(WZ = WX+XY + YZ\) (from line 2), we substitute \(UX\) and \(WZ\) in the equation \(UX = WZ\). This is substitution, not addition property of equality.

Step2: Correct reason

The substitution property of equality states that if \(a = b\) and \(a=c\), then \(b = c\). Here, since \(UX=WZ\), and \(UX\) is expressed as \(UV + VW+WX\) and \(WZ\) as \(WX+XY + YZ\), we substitute \(UX\) and \(WZ\) in \(UX = WZ\) to get \(UV + VW+WX=WX + XY + YZ\).

Answer:

The reason in line \(3\) does not justify the statement because \(UX\) and \(WZ\) are substituted. Instead, the reason should be the substitution property of equality.