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? (4 points)


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

Answer 2

plas halp

Answer 3

The statements made above are all geometrically correct.

Answer 4

If you follow the statements and the angles, you will notice that m<1=m<2 is correct. But since one is greater than the other, the lines cannot be parallel.

Answer 5

As far as the question of logic is concerned, it was used to contradict the assumption made.