PLZ PLZ PLZ HELP ME! come on its worth 2 pts?

Question

Can you name ways to prove two lines are parallel? Best answer gets 12 pts, and everybody gets 2! lol :-) thanks sooo much for answering!!!

well im doing a proof, and its not on a grid so i cant do slope. its like a square with diaganols in it.

Answer 1

There are lots of ways to prove lines parallel. It depends on what you
are given to work with. Are you using coordinates and equations in
algebra, or drawing lines and looking for similar angles in geometry?

I'll get you started by listing a couple of different ways to prove
lines parallel, using several different methods.

1. SLOPE

If both lines have the same slope, they are parallel. So, if you know
the equations for both lines, and you can see that both equations have
the same slope, you know the lines are parallel.

2. USING OTHER LINES - Similar angles

Suppose we have three lines again all in the same plane, A, B and C.
If line B makes a 30-degree angle on the left with line A, and also a
30-degree angle on the left with line C, then A and C are parallel.
This method can also be applied for lines that are perpendicular (form
90-degree angles).

Here is something else to keep in mind. Remember that parallel in 3
dimensions is more complicated than parallel in 2 dimensions. In 2
dimensions, if two lines never intersect, you know they are parallel.
In 3 dimensions, it is possible to have two lines that never intersect
but are not parallel. This is called skew.

Answer 2

That depends on whether you're in Euclidean geometry or analytic geometry. or even in non Euclidean geometry.
I assume you're in Euclidean geometry, since you've said you don't have a grid, you only have a square with diagonals.
The main ideas you'd want to use involve distance or angles.
Parallel lines are the same distance apart everywhere. If you can prove that your lines are the same distance apart when observed at various points, that would do it. You say you have something like a square. If your are given, or if you can prove, that you have a square, that is, a figure with four equal sides, that would give you your equal distances.
Parallel lines cut by transversals (your diagonals) have all sorts of pairs of equal and supplementary angles. If you can prove any of the relevant pairs to be equal or supplementray, that would do it.
Here's a nice website that illustrates this with animation:
http://www.mathopenref.com/parallel.html

Answer 3

1). Write their equations in the form y = mx+ b
and see if they have the same slope or if both
are vertical.

2. Cross both lines with a transversal and see
if the corresponding angles or alternate interior
angles or alternate exterior angles are congruent.

3. Two lines are parallel if there exists a slide
which carries one to the other.

Answer 4

Here are FOUR ways:

1A. and 1B. Geometrically, they are parallel if a transversal (that is, a straight line that crosses them both) makes the same (corresponding) angle with both of them where it crosses them.

For example, lay a stick across two railway lines at an acute angle measured clockwise from the stick to one railway line; then it will make the same acute angle, measured clockwise in the same way, to the other railway line.

In fact, the concept of "measured clockwise" covers two cases often introduced distinctly in geometry classes:

1A. where the two (acute) angles (say) are on the SAME SIDE of the transversal (think of a 'not equals' sign, ' ≠ ', and how there are two similarly placed acute angles on each side of the transversal), and

1B. where the acute angles are on OPPOSITE sides of the transversal (like a 'Z').

1C. This is essentially a corollary of 1A. and/or 1B. If the TWO "inside angles" made by the pair of lines at opposite ends of the transversal are supplementary (i.e., add up to 180 deg. or pi radians), then the two lines are parallel.

(So, in the ' ≠ ' sign, if you approach the transversal along one of the two horizontal lines, turn to go along the transversal, and then go back along the other horizontal line, now travelling in the OPPOSITE DIRECTION to the one you started with, you will have turned through the sum of what I call the two "inside angles," and THAT SUM will be 180 deg. or pi radians.)

Later: I've just seen your "additional details." Your "diagonals" might be what I called "transversals."

2. In coordinate geometry, a line is given by y = m x + c, where 'm' is the 'slope' of the line. Two lines are parallel if their slopes, m_1 and m_2, say, are equal. That slope is tan(theta), where theta would be the angle made with respect to the direction of the x-axis, in the very first way I gave.

Live long and prosper.

Answer 5

Write the equations of the line in the form of y=mx + b

If the m value(the slope) is the same for both, then the two lines are parallel, and will never intersect.

Answer 6

1) Two lines are parallel if they have the same slope.

2) Two lines are parallel if they are both perpendicular to the same line.

Answer 7

The lines, if drawn out to infinity, never cross

The lines have the same slope

Answer 8

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Answer 9

hw abt best answer anyways if 2 lines have the same slope they are parallel
n slope is nagative coeffof x/coeff of y in eqn
ax+by+c=0
slope=-a/b

Answer 10

OK here it goes parallel lines that extend alongside one another,always equidistant and never meeting at infinity.