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

Question

asked Nov 7, 2019 213k views

1 Answer

Ali Husham · Answer 1 · 2019-11-12T14:19:55+0000

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.