i really don't understand how to realate an angle formed by a transversal and two parallel line (please need help understanding fast!!:0)

A straight line transversing (intersecting) two parallel lines creates the same set of angles at both intersections.

See
http://library.thinkquest.org/20991/geo/parallel.html
for an illustration

I'd be happy to help you understand how to relate an angle formed by a transversal and two parallel lines.

To begin, let's define the terms involved:
- Transversal: A line that intersects two or more other lines at different points.
- Parallel lines: Lines that are always the same distance apart and never intersect.

When a transversal intersects two parallel lines, it creates several angles. The important relationship to remember is that corresponding angles, alternate interior angles, and alternate exterior angles are congruent.

Here's how you can determine the relationships between angles formed by a transversal and two parallel lines:

1. Corresponding angles:
- Corresponding angles are located on the same side of the transversal and at the same relative position with respect to the parallel lines.
- To find corresponding angles, identify the pair of angles that are in the same position on either side of the transversal.
- Corresponding angles are always congruent, which means they have the same measure.

2. Alternate interior angles:
- Alternate interior angles are located on opposite sides of the transversal and inside (between) the parallel lines.
- To find alternate interior angles, identify the pair of angles that are inside (between) the parallel lines and on opposite sides of the transversal.
- Alternate interior angles are always congruent.

3. Alternate exterior angles:
- Alternate exterior angles are located on opposite sides of the transversal and outside (beyond) the parallel lines.
- To find alternate exterior angles, identify the pair of angles that are outside (beyond) the parallel lines and on opposite sides of the transversal.
- Alternate exterior angles are always congruent.

Remember, these relationships hold true only when the lines being intersected by the transversal are parallel. If the lines are not parallel, these angle relationships will not be valid.

I hope this explanation helps you understand how to relate the angles formed by a transversal and two parallel lines. If you have any further questions, feel free to ask!