How Do You Determine If Two Lines Are Parallel?
Parallel lines are two lines that run along the exact same angle and, as such, never intersect no matter how long they run. Parallel lines also have certain angle relationships that can be used to prove that they are parallel when they run along each other. Specifically, when two parallel lines are both intersected by a third line (a transversal), angles in the same position in relation to the transversal (complementary angles) have the same measurement (are congruent), which can be assembled into a mathematical proof.
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Instructions
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Take two parallel lines running alongside each other or draw two such lines to begin the proof. This proof can either be used to verify that two lines are parallel or to draw two such lines by slightly adjusting the second line once the geometric relationship has been established.
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Draw a third line that intersects the two previous lines. This line will create two angles with each of the two previous lines and those angles can be used to establish a parallel relationship with the lines.
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Measure the angles on the same side of the line formed by the intersections and in the same position with respect to the original lines (complementary angles). Use either a protractor if you are using graph paper or an angle measuring application in the case of a computer program.
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When the two lines are intersected, you will have a figure like an "H". Be sure that you are measuring one angle at each intersection on the same side, as a different set of relationships exists between opposite angles. For instance, the angle above the middle stick and to the left of the "H" is complementary to the angle above the middle stick and just to the left of the last vertical line in the "H", inside the letter.
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Compare the two measurements. If the lines are parallel, the two complementary angles should have the exact same measurement.
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If you are trying to draw two parallel lines, you can use this geometric relationship to slightly adjust one of the angles and redraw the second line to meet this criteria.
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Tips & Warnings
Be sure to use a pencil rather than a pen as you might have to redraw the second line.
It's very important that you measure angles on the same side of the intersection and in the same position. If you have trouble distinguishing the sides, draw a second line to intersect the two parallel lines, forming a quadrilateral, and use the shape to make sure you are either measuring the two angles inside or outside the shape.
References
Resources
- Photo Credit city geometry image by araraadt from Fotolia.com
