# Parallel Lines

Parallel lines are lines that are always the same distance apart from one another, and no matter how far they are extended, they never cross. Parallel lines have the same slope, and can be drawn in any direction.

When we talk about parallel lines, we often have another line called a transversal. A transversal is just another line that crosses over both parallel lines.

The angles created by a transversal crossing parallel lines have special names:

• corresponding angles: angles in the same position within the parallel lines
• alternate interior angles: angles inside the parallel lines, on opposite sides of the transversal
• supplementary angles: angles that add up to 180º

Examples of these types of angles:

Corresponding Angles: Note that angles 1 & 2 and 3 & 4 are both in the same position as each other. 1 & 2 are both above a parallel line, and to the left of the transversal. 3 & 4 are both below a parallel line, and to the right of the transversal.

Alternate Interior Angles: Note that all the angles are within the parallel lines. 1 & 2 are within the parallel lines and are on opposite sides of the transversal. 3 & 4 are within the parallel lines and are on opposite sides of the transversal.

Supplementary Angles: These angles need to add up to 180º. Note that 1 & 2 are both on the same line, with a transversal dividing them. 3 & 4 are also on the same line, with one of the parallel lines dividing them.

When you are asked to find the measurement of one angle while given the measure of another, keep in mind what you know about straight lines. A straight line makes 180º. Knowing that will help you determine the angle measurements of of any angle within parallel lines and a transversal.

When only one angle measurement is given, but we can still find all the other measurements.

Keep in mind vertical angles: angles that share the same vertex and are made up of the same lines.

The only angle we know is 52º. Use the above relationships between angles to find all the missing angles:

angle a: a is a corresponding angle to 52º. Corresponding angles are equal so a = 52º.

angle b: b is not directly related to 52º but it forms a straight line with angle a so they must add up to 180º. If angle a is 52º then 180 – 52 = 128. Therefore b = 128º.

angle c: c is also not directly related to 52º but it is a vertical angle to angle b. We could also say that it forms a straight line with angle a. Either way, c = 128º.

angle d: d is an alternate interior angle to 52º, therefore d = 52º.

angle e: e forms a straight line with 52º so again we know they add up to 180º. Again, 180 – 52 = 128º. Therefore e = 128º.

angle f: f is a vertical angle to angle e, and it makes a straight line with 52º. Either way, f = 128º.

angle g: g is a vertical angle to 52º so g = 52º.