Five Ways to Prove That Two Lines Are Parallel

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Parallel lines will never intersect. These lines will be the exact same distance apart in the same plane. A plane is two-dimensional, and it can have infinite width and length. Whether you are on a rowing team, working on a building project or just working on a math problem, you will need to know if your lines are parallel. Insert a straight line that intersects both lines, called a transversal, to determine if they are parallel.

Alternate Exterior Angles

  • Using a compass, you can measure the angles created by the parallel lines and the transversal, or the line that intersects the two parallel lines. Measuring the exterior angles, the angles on the top of the first parallel line and the bottom of the second parallel line, can tell you if your lines are parallel. If the angle on the top and to the left of the transversal line is the same size as the angle on the bottom and to the right of the transversal line, the lines are parallel. This is also true for the angle on the top and to the right of the transversal and the angle on the bottom and to the left of the transversal. If these are the same, the lines are parallel.

Alternate Interior Angles

  • Look between the two lines, the bottom of the first and the top of the second. If the angles that are on opposite sides of the transversal are equal, the lines are parallel. For instance, if the bottom left of the first parallel line and the top right angle of the second are equal, the lines are parallel. The same is true of the opposite angles. The angle at the bottom right of the first parallel line and the top left of the second should be equal for the lines to be parallel.

Corresponding Angles

  • Corresponding angles are the angles created in the same area on each parallel line when they are intersected by a transversal line. For instance, the top right side of the where first parallel line and the transversal intersect and the top right side of the intersection of the second parallel line and transversal are corresponding angles. When the corresponding angles, the angles on the same side of the transversal and the same side of each parallel line, are equal, then the two lines are parallel.

Consecutive Interior

  • If the two angles between the line and on one side of the transversal add up to 180 degrees, the lines are parallel. Test this theory by adding the angles of the left side of the transversal line that are between the two parallel lines. Then test it on the two angles on the right side of the transversal. If both are 180, you have parallel lines.

Consecutive Exterior

  • Add the angles on the top and bottom of the same side of the transversal line. If the angles add up to 180, you have parallel lines. For instance, add the angle that is on the top of the first parallel line to the left of the transversal to the angle on the bottom of the second parallel line that is to the right of the transversal, and it should equal a 180-degree angle. The same is true for the angle at the top of the first parallel line and to the right of the transversal and the angle under the second parallel line to the right of the transversal.

References

  • Photo Credit Jupiterimages/Photos.com/Getty Images
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