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Vertical Angle Theorem 3313 Views


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Description:

This video explains the vertical angle theorem. Learn about supplementary angles, adjacent angles, and linear pairs, plus bungee jumping. Intersecting lines have never been more fun.

Language:
English Language

Transcript

00:03

Vertical Angle Theorem, a la Shmoop.

00:06

Mr. and Mrs. Thimbleton have just celebrated their sixty-third wedding anniversary. [Mr. and Mrs. Thimbleton in front of a big love heart]

00:11

They're in the prime of their lives and just as in love as they were all those years ago.

00:17

They're also just as thrill-seeking as they were back then too.

00:20

So to celebrate, these eighty-two year old daredevils decided to go bungee jumping together.

00:25

If they both jump in opposite directions and don't hit each other… [The Thimbleton's bungee jump off a bridge]

00:30

…they'll make vertical angles.

00:32

If the angle the bungee cords make at the very top is 52 degrees…

00:37

…what angle will they make at the bottom?

00:40

To start, let's look at Mr. Thimbleton's bungee cord. [Mr. Thimbleton hanging down from the bridge]

00:45

Since it's a straight line, we know it makes a 180 degree angle.

00:49

That means our top angle plus this angle on the side make a linear pair…

00:54

…two angles that are supplementary and adjacent.

00:59

Since they’re supplementary, we know they add up to 180 degrees.

01:03

And because we know the top angle is 52 degrees, we can find the side angle by subtracting

01:09

180 minus 52.

01:12

The angle on the side is 128 degrees.

01:16

We're looking for the measure of the very bottom angle.

01:19

Let's consider Mrs. Thimbleton's bungee cord. [Mrs. Thimbleton hangs from the bridge]

01:23

It also makes a 180 degree angle, which means the side angle we just found and the bottom

01:28

angle also add up to 180 degrees.

01:31

If we take 180 minus 128, we end up with 52 degrees as the measure of the bottom angle.

01:39

Let's find the measure of the last angle. [Mr. Thimbleton pointing to the angle with his cane]

01:41

If we go through the same process and pick out a supplementary linear pair…

01:45

…we'll calculate 180 degrees minus 52 degrees equals 128 degrees.

01:51

So really, vertical angles are any two opposite angles formed by intersecting lines.

01:58

And the vertical angle theorem says that vertical angles are congruent… in other words, their [Mr. Thimbleton stood in front of a blackboard]

02:04

angles are equal.

02:05

Is this true?

02:07

Here we have two pairs of vertical angles:

02:09

The top and bottom, each measuring 52 degrees, and on the right and left, each measuring

02:15

128 degrees.

02:17

So yes.

02:18

Vertical angles, even if they're horizontal, are congruent.

02:22

Now you can be as secure with your knowledge of vertical angles as the Thimbletons are [The Thimbleton's jump off the bridge again and their dentures fall out]

02:27

to their huge bungee cords.

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