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This video is provided as supplementary material
for courses taught at Howard Community College and in this video
I'm going to do a proof that vertical angles
are equal. This is fairly easy proof.
Here's how it goes. I've drawn two
intersecting lines and at they place where they Intersect
I've labeled the four angles A, B,C, and D.
Now angle A is opposite
to angle C. When we have two angles that are opposite each other we call them
vertical angles.
I've got two other vertical angles here:
angle B is opposite angle D,
so they're also vertical angles. What I want to do is prove that angle A
equals angle C. So here's how I'll do it.
Angle A and angle B
are adjacent angles and they both lie
along the same line. So they are supplementary angles.
We know that supplementary angles equal,
or add up to 180 degrees.
So angle A plus angle B
equal 180 degrees.
Now angle B and angle C also lie along the same line
and are adjacent to each other, so they add up to 180 degrees.
They're supplementary. So angle B
plus angle C equal
180 degrees. Now I've got two equations
and what I'm going to do is, for each equation, I'm going to subtract
angle B from both sides. So that first equation,
angle A plus angle B equal 180 degrees
is now going to become angle A
equals 180 degrees
minus angle B.
And the second equation, angle B
plus angle C equals 180 degrees,
is going to become angle C
equals 180 degrees
minus angle B.
And now let's subtract both of those equations. We'll subtract
the angle C equation
from the angle A equation. I'm going to end up with
angle A minus angle C
equals... let's see:180 degrees minus 180 degrees is zero.
And I've also got angle B and angle B. So when I subtract,
on the right side of the equations, I'll end up with zero.
So I've got angle A minus angle C equals zero.
Let's just add angle C to both sides. And I'll get
angle A equals
angle C, which is what we set out to prove.
So there's the proof that vertical
or opposite angles will be equal to each other.
Take care, I'll see you next time.