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Proving Lines are Perpendicular 795 Views
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Description:
Prove it, Shmoopers. We dare you.
Transcript
- 00:04
Proving Lines are Perpendicular, a la Shmoop.
- 00:10
Leroy, the city pigeon, is having a bit of a tiff with his country cousin, Roy Lee.
- 00:15
Leroy argues that the streets below form a perfect cross…
- 00:23
…but Roy Lee insists that the streets look kind of… slanted.
- 00:30
How can Leroy prove that the streets do, in fact, form a perfect cross,
Full Transcript
- 00:34
and that they’re perpendicular?
- 00:36
First let’s think about the streets as two intersecting lines on a map.
- 00:41
Then we can use some useful theorems that will help us determine if the lines are, in
- 00:45
fact, perfectly perpendicular.
- 00:49
If two lines are perpendicular, they’ll form four right angles at their intersection.
- 00:56
Right angles measure 90 degrees, and it appears that Leroy’s two streets create four right
- 01:02
angles at their intersection.
- 01:04
But Leroy wants to make sure.
- 01:08
Another theorem Leroy can use follows the same principle:
- 01:11
It says “If two lines intersect to form a linear pair of congruent angles,
- 01:17
then the lines are perpendicular.”
- 01:19
Angles 1 and 4 are adjacent and form a linear pair.
- 01:23
Two angles in a linear pair are always supplementary,
- 01:25
which means that their measures must add to 180 degrees.
- 01:29
That means the measure of angle 1 plus the measure of angle 4 equals 180 degrees.
- 01:35
If these angles have to be congruent, their measures should to be equal to each other.
- 01:39
So let's substitute the measure of angle 4 with the measure of angle 1.
- 01:43
They're both equal anyway, right?
- 01:46
We can add the measure of angle 1 and the measure of angle 1 to get 2 times the measure of angle 1.
- 01:52
To isolate the measure of angle 1, we can divide 2 by both sides
- 01:56
and get that the measure of angle 1 is 90 degrees.
- 01:59
Because the two angles are congruent, we know that 90 degrees must also be the measure of angle 4.
- 02:04
Since our 90 degree angles are a linear pair of congruent angles, like the theorem says,...
- 02:10
...we know the lines are perpendicular. Voila!
- 02:13
He even uses a protractor to be certain.
- 02:16
Looks like this theorem reinforces Leroy’s argument.
- 02:21
Leroy was indeed correct… the streets ARE perpendicular.
- 02:25
Oh, great. Now he’s going to do that obnoxious “victory strut” stuff.
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