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Proving Lines are Perpendicular 795 Views


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Description:

Prove it, Shmoopers. We dare you.

Language:
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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,

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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