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Parallel Lines, Transversals, and Angles, a la Shmoop.

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There are some couples who are just destined to be together forever.

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Romeo and Juliet. Cinderella and Prince Charming. Paula Deen and butter.

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But the greatest couple of them all has to be…

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…parallel lines. Parallel lines never touch, but they always

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stand by their partner. They stay by each other's sides forever. That's love.

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Besides, it's more romantic than having one wild encounter and then parting ways afterwards.

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When a transversal cuts across two parallel lines, it forms eight angles.

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If the measure of angle 1 is 110 degrees, what are the measures of the other 7 angles?

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Sounds like a lot of work, but it's not as bad as you might think.

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First, we can see that angles 1 and 3 are vertical angles, and we know that vertical

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angles are always congruent… in other words, they have equal measurements.

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So angle 3 has a measure of 110 degrees, too.

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It also helps to know that corresponding angles…

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…or angles that are in the same position relative to the parallel lines and the transversal…

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…are also congruent.

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In this case, the corresponding angle to angle 1 is angle 5…

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…because it's above the parallel line and to the left of the transversal. So angle 5

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is also 110 degrees. Wait. So angles 3 and 5 are congruent, too?

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Actually… yes.

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They're both on the interior between the two parallel lines and on alternate sides of the

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transversal, so we call them alternate interior angles.

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All alternate interior angles are congruent. There's one more angle that's 110 degrees,

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and that's angle 7.

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Angle 1 and angle 7 are both on the exterior of the parallel lines and alternate sides

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of the transversal, so they're called alternate exterior angles.

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Alternate exterior angles are also congruent, and we can check that using vertical angles

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or corresponding angles.

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Yup, looks like 110 degrees to us. Those are all the odd angles, but what about

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the evens? We know that a straight angle, or a line,

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has 180 degrees.

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Since any even angle makes a linear pair with an odd angle, any even angle is supplementary

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to an odd angle.

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That means the even angles have a measure of 180 minus 110… or 70 degrees.

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And ta-da! You now have all your angles. So don’t forget to include parallel lines

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when listing the world’s great love stories.

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And as a bonus tip… don’t ever try to get between Paula Deen and her butter.

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