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, m, x, y, z in order)

statements	reasons
2. (ux=uv + vw+wx); (wz = wx+xy + yz)	2. segment addition
3. (uv + vw+wx=wx + xy+yz)	3. addition property of equality
4. (uv + vw=xy + yz)	4. subtraction property of equality
5. (vw = xy)	5. given
6. (uv = yz)	6. subtraction property of equality

where is the first error in this proof?
the reason in line does not justify the statement because instead, the reason should be |

Explanation:

Step1: Analyze line 3 reasoning

The given reason for line 3 is "addition property of equality", but we are substituting the segment addition expressions from step 2 into the given equality from step 1. This is the substitution property, not addition property.

Step2: Identify the error location

Line 3's reason is incorrect. The statement uses substitution of the segment sums into the original equality, not the addition property of equality.

Step3: Correct the reason

The correct reason for line 3 is the substitution property of equality, as we replace $UX$ and $WZ$ with their segment addition equivalents in the equation $UX=WZ$.

Answer:

The flaw is in line 3.
The reason in line 3 does not justify the statement because the addition property of equality applies when adding the same value to both sides, but here we are substituting equivalent expressions. Instead, the reason should be substitution property of equality.