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Vertical Angle Theorem 3320 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.
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.
Full Transcript
- 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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