Congruent
Yes, a transversal line always intersects two parallel lines.
Yes a rectangle is parallel because it has lines that are the same so they always will be parallel.
False.
A four-sided polygon with two parallel sides is called a trapezoid. In a trapezoid, the two parallel sides are known as the bases, while the non-parallel sides are called the legs. The parallel sides of a trapezoid are of different lengths, distinguishing it from a parallelogram where both pairs of opposite sides are parallel and equal in length. The sum of the interior angles of a trapezoid is always equal to 360 degrees.
A parallel line is two lines along the same path in the same direction. Also parallel lines always have to be straight Some examples of parallel lines are below. \ | | / / = ll
yes because they will always equal 180 degrees, regardless of the angle at which the transversal intersects the two parallel lines
Those are "alternate interior" angles. They're always equal.
Alternate and interior angles are created between parallel lines when a transversal line cuts through them.
Yes. "Alternate interior" angles are always interior. Angles that are not interior as well as alternate are never accurately described as "alternate interior" angles.
The corresponding and alternate angles
They are always equal on the transversal line that cuts through parallel lines
Yes, a transversal line always intersects two parallel lines.
Wrong statement. Parallel lines don't always make vertical angles without the transversal, the line that passes through these lines. Without the transversal, we can't make the conclusion that parallel lines form vertical angles.
The angles that share a vertex and a side of a transversal but no interior points are called vertical angles. Vertical angles are formed when two lines intersect, and they are always congruent.
A transversal line that cuts through parallel lines creates corresponding angles that are equal but can vary in sizes
No, two lines would not be parallel if the consecutive interior angles measured 108 degrees and 74 degrees. Consecutive interior angles on parallel lines are always congruent, meaning they have the same measure. Therefore, if the consecutive interior angles have different measures, the lines cannot be parallel.
I understand your question to be, "Is it true that parallel lines are everywhere equidistant and never intersect?" In what follows, I assume we're talking about a two-dimensional plane. By definition, two lines that are parallel (in the same plane) never intersect. In Euclidean (AKA Parabolic or simply E) Geometry, and also in Hyperbolic (AKA simply L) Geometry, parallel lines exist. In Elliptical (AKA R) Geometry, all lines eventually intersect so parallel lines do not exist. Now, are two parallel lines (in the same plane) everywhere equidistant? If so, that means that it is possible, at any point on one of the lines, to construct a perpendicular that will meet the other line in a perpendicular, and that the length of the segments constructed will be always the same. In Euclidean Geometry, two parallel lines (in a plane) are indeed everywhere equidistant. To prove it requires the converse of the Alternate Interior Angles theorem (AIA), which says that if two parallel lines are cut by a transversal, the alternate interior angles will be congruent. Note that this is the CONVERSE of AIA, not AIA. Some people get this mixed up. In Hyperbolic Geometry, two lines can be parallel, but be further apart some places than others. I know that sounds rather odd, if you're not used to it. Here's an image that might help: imagine that your plane is a thin sheet of rubber, and for some reason is being stretched. The further you go from your starting point, the more it stretches, and it's always stretching away from you. This means that your parallel lines will keep getting further and further apart.