Lines m and n are cut by a transversal, as shown in the figure.

Line l is drawn from the upper left to lower right. Lines m and n are drawn from the upper right to the lower left. Line l intersects line m and lines n. Where line l intersects line m, the angles formed are listed from the top in clockwise order: angle 1, angle 2, angle 3, and angle 4. Where line l intersects line n, the angles formed are listed from the top in clockwise order: angle 5, angle 6, angle 7, and angle 8.

Given line m is not parallel to line n, prove ∠3 is not congruent to ∠5 by contradiction. (2 points for the assumption statement, 4 points for the remainder of the proof)

Question

Lines m and n are cut by a transversal, as shown in the figure.

Line l is drawn from the upper left to lower right. Lines m and n are drawn from the upper right to the lower left. Line l intersects line m and lines n. Where line l intersects line m, the angles formed are listed from the top in clockwise order: angle 1, angle 2, angle 3, and angle 4. Where line l intersects line n, the angles formed are listed from the top in clockwise order: angle 5, angle 6, angle 7, and angle 8.

Given line m is not parallel to line n, prove ∠3 is not congruent to ∠5 by contradiction. (2 points for the assumption statement, 4 points for the remainder of the proof)

Axolotl · Answer

Picture for better understanding

Axolotl · Answer

This is what I have: ∠3 and ∠5 are congruent. ∠3 = ∠5 and ∠8 = ∠2. If alternate interior angles are equal, the two lines must be parallel. This is the opposite of what was described in the point.

Does it sound good?

Axolotl · Answer

@gucchi you there? I have to go so please answer now if you thinks the answer I have is good.

Gucchi · Answer

@axolotl wrote:

This is what I have: ∠3 and ∠5 are congruent. ∠3 = ∠5 and ∠8 = ∠2. If alternate interior angles are equal, the two lines must be parallel. This is the opposite of what was described in the point. Does it sound good?

this looks good and well detailed

Axolotl · Answer

@gucchi wrote:

@axolotl wrote:

This is what I have: ∠3 and ∠5 are congruent. ∠3 = ∠5 and ∠8 = ∠2. If alternate interior angles are equal, the two lines must be parallel. This is the opposite of what was described in the point. Does it sound good?

this looks good and well detailed

OK yay! TYSM for your response. I gtg. Bye!!

Gucchi · Answer

np!!

Gucchi · Answer

i cant believe you actually gotta do this

Gucchi · Answer

😭

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