Which is the most logical order of statements and reasons i, ii, and iii to complete the proof?

Asked by maham237 @ 16/12/2020 in Mathematics viewed by 334 People

Answered by maham237 @ 16/12/2020

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.

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