Question

Given lines l and m that are intersected by line t where m∠1 > m∠2, the following is an indirect paragraph proof proving lines l and m are not parallel.

Answer 1

Assume lines l and m are parallel. According the Transitive Property of Equality, angle 1 is congruent to angle 2. Angle 1 is congruent to angle 3 by the Corresponding Angles Theorem. Angle 3 is congruent to angle 2 by the Vertical Angles Theorem. And, by the definition of congruence, m∠1 = m∠2. This contradicts the given statement that m∠1 > m∠2. Therefore line l is not parallel to line m.
Is the indirect proof logically valid? If so, why? If not, why not?

Answer 2

Select one:
a. Yes. Statements are presented in a logical order using the correct theorems.
b. Yes. The conclusion was used to contradict the assumption.
c. No. The conclusion was used to contradict the assumption.
d. No. The progression of the statements is logically inaccurate.

Answer 3

@ganeshie8 @Hero @myininaya

Answer 4

YEA IM BACK

Answer 5

@Hero

Answer 6

It appears to be "D". It makes no sense to use a transitive property if no previous relationship has been established.

Should be

\(\angle{1} \cong\angle{3} \)
\(\angle{3} \cong\angle{2} \)
Therefore, by transitivity
\(\angle{1} \cong\angle{2} \)