help with math..MATH GENIUSES!?

Question

tell whether the statement is always, sometimes, or never true.

1) if 2 distinct lines intersect, then they are parallel.
2)if 2 distinct lines do not intersect, then they are parallel.
3)if 2 angles are alternate interior angles, then they are on opposite sides of the transversal
4)if 2 parallel lines are cut by a transversal, then the alternate interior angles are congruent.
5)if 2 parallel lines are cut by a transversal, then the alternate interior angles are complementary
6)if 2 parallel angles are cut by a transversal, then the corresponding angles are complementary

6) not parallel angles= its parallel lines..my baddd

Answer 1

1) if 2 distinct lines intersect, then they are parallel.
never true

2)if 2 distinct lines do not intersect, then they are parallel.
sometimes.they can be skew

3)if 2 angles are alternate interior angles, then they are on opposite sides of the transversal
always true

4)if 2 parallel lines are cut by a transversal, then the alternate interior angles are congruent.
always
true
5)if 2 parallel lines are cut by a transversal, then the alternate interior angles are complementary
sometimes- if they bothare 45*

6)if 2 parallel lines are cut by a transversal, then the corresponding angles are complementary
some times -if they both are 45

Answer 2

For plane geometry (Euclidean):

1) Never ever true. Parallel lines never intersect so lines that intersect cannot be parallel.

2) Always true. This is in fact the very definition of parallel lines.

3) Always true. That is why they are alternate interior angles.

4) Always true.

5) Sometimes true by happenstance (i.e.: it has nothing to do with the fact they are alternate interior angles, just the chance they happen to be the right measure (45 degrees))

6) Not sure what you mean here because I never heard the term corresponding angles. However, if by that you mean the angles inside the parallel lines where cut by the transversal, then never true because they are supplementary, not complementary. If by that you meant the angles one could describe as "every other angle" or the angle above both parallel lines at the transversal on the same side (or below), then like in 5) sometimes true but only by chance. Of course, use congruency to apply the two possibilities here to all the other angle-pair possibilities.

Answer 3

1. never true.. parallel lines never intersect
2. sometimes true..if two distinct lines do not intersect, they might be parallel or skew
3. always true..all the interior angles are onopposite sides
4. always true...transversal always cut parallels and alternate interior angles are congruent
5. sometimes true... sometimes the sum of the alternate interior angles is 90 degrees, sometimes, not...
6. sometimes true...if each measures 45 degrees...

Answer 4

1) Never true. Parallel lines never intersect.

2) Always true. See above.

3-6. OK, you got me there. I never heard of a transversal.

Answer 5

Hello

1) never true ( if two lines intersect they Are not parrallel : Pararrel lines never intersect )

2)alway true ( see question One )

3)always true

4) alway true
5) alway true
6)alway true

Answer 6

1. never
2. sometimes
3. always
4. always
5. sometimes
6. and... wha? 2 parallel angles??

Answer 7

1.) never
2.) sometimes
3.) always
4.) always

not really sure about 5 & 6

Answer 8

Come on you'll keep flunking if you don't do your own work.