Question

Which is the most logical order of statements and reasons I, II, and III to complete the proof?

Answer 1

Observe the figure.

After the given statements as:

Statement 1:
`UV\parallel WZ`

Statement 2: Points S,Q,R and T are all lie on the same plane.

Statement 3:
`m \angle SQT = 180^\circ`

Statement 4:
`m \angle SQV + m \angle VQT = m \angle SQT`

Statement 5:
`m \angle SQV + m \angle VQT =180^\circ`

Now, the next statement is as:

Statement 6:
`m \angle VQT + m \angle ZRS =180^\circ` which is statement III.

(Same side interior angles theorem)

Statement 7:
`m \angle SQV + m \angle VQT=m \angle VQT + m \angle ZRS` which is statement II.

(Substitution property of equality)

Statement 8:
`m \angle SQV + m \angle VQT-m \angle VQT=m \angle VQT + m \angle ZRS-m \angle VQT`

`m \angle SQV = m \angle ZRS`which is statement I.

(Subtraction property of equality)

So, the correct order of the given reasons to complete the proof is III, II, I.

Therefore, Option 4 is the correct answer.