Question

Geometry help please? <3

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.
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?

Answer 1

This photo was attached.

Answer 2

This statement is not true based on the flow of the given argument:

According the Transitive Property of Equality, angle 1 is congruent to angle 2.

Answer 3

If lines l and m are intersected by line t where m∠1 > m∠2, then l and m are not parallel.

Indirect Proof - Assume the negation of l and m are not parallel and attempt to show that this assumption contradicts the hypothesis: m∠1 > m∠2.


Assume lines l and m are parallel.

Angle 1 is congruent to angle 3 by the Corresponding Angles Theorem.

Angle 3 is congruent to angle 2 by the Vertical Angles Theorem.

According the Transitive Property of Equality, angle 1 is congruent to angle 2.

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.


The above is how the logic in the proof should flow ^^^^

One step was out of place. See what you think. @CarinaSarfati