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

Explanation:

Step1: Analyze line 3

Line 3 states \(UV + VW+WX = WX + XY + YZ\). Since \(UX = WZ\) (given) and \(UX=UV + VW+WX\), \(WZ = WX + XY + YZ\) (segment addition), we substitute \(UX\) with \(UV + VW+WX\) and \(WZ\) with \(WX + XY + YZ\) in the equation \(UX = WZ\).

Step2: Check the reason for line 3

The addition property of equality states that if \(a = b\), then \(a + c=b + c\). But here, we are not adding the same quantity to both sides. We are substituting \(UX\) and \(WZ\) with their segment - addition expressions.

Answer:

The reason in line \(3\) does not justify the statement because we are not using the addition property of equality. Instead, the reason should be the substitution property of equality.