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To prove lines are parallel, you need a third line. We at Shmoop (and the rest of the world) call it a transversal.
Proving Lines are Parallel 1113 Views
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Description:
To prove lines are parallel, you need a third line. We at Shmoop (and the rest of the world) call it a transversal.
Transcript
- 00:05
Proving Lines are Parallel, a la Shmoop.
- 00:10
On the forest floor, tensions are brewing.
- 00:13
It seems two snails are in the midst of a heated argument.
- 00:17
They are worried that their paths on the forest floor may cross; if that happens, they might
- 00:22
crash. And they just let their insurance lapse.
Full Transcript
- 00:26
But hang on a sec; do they really have to be worried in the first place?
- 00:32
By definition, parallel lines never cross, even if they go on forever.
- 00:36
If we can prove that these snails’ paths are parallel to each other…
- 00:39
…then they can stop arguing and leave the forest undergrowth in peace.
- 00:43
We’ve got several important theorems and postulates to help us out.
- 00:47
All of those theorems and postulates have to do with transversals…
- 00:51
…a third line cutting across the two lines in question.
- 00:56
A straight branch lies across the snails’ paths… that can serve as our transversal.
- 01:02
A transversal will create 8 different angles we should examine before reaching our conclusion.
- 01:09
The first postulate we can use to determine whether two lines are parallel is the Corresponding
- 01:18
Angles Converse, which states that…
- 01:25
…“If two lines are cut by a transversal so that corresponding angles are congruent,
- 01:30
then the lines are parallel.”
- 01:39
Remember that corresponding angles refer to angles such as 2 and 6, or 3 and 7.
- 01:45
Check. The first theorem we can use is the Alternate
- 01:45
Exterior Angles Converse, which states…
- 01:46
…“If two lines are cut by a transversal so that alternate exterior angles are congruent,
- 01:52
then the lines are parallel.”
- 01:53
Remember that alternate exterior angles refer to angles such as 2 and 8, or 1 and 7.
- 01:56
Check. The second theorem we can use is the Consecutive
- 01:59
Interior Angles Converse, which states…
- 02:02
…“If two lines are cut by a transversal so that consecutive interior angles are supplementary…
- 02:11
meaning they add up to 180 degrees… then the lines are parallel.”
- 02:17
Consecutive interior angles, in this case, refer to angles 3 and 6.
- 02:20
The branch creates consecutive interior angles measuring 150 degrees and 30 degrees; 150
- 02:28
plus 30 is 180.
- 02:32
Check. The last theorem we can use is the Alternate
- 02:40
Interior Angles Converse, which states…
- 02:46
…“If two lines are cut by a transversal so that alternate interior angles are congruent,
- 02:52
then the lines are parallel.”
- 02:54
Alternate Interior Angles refer to angles 4 and 6 or 3 and 5.
- 02:54
Check-a-rooni. It seems those snails don’t have to worry
- 02:58
about crashing into each other after all.
- 03:00
But they just might run into a few more transversals on their journey.
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