So, this is from angle side angle congruency

If we knew that this angle is equal to that angle and that angle is equal to that angle, we'd be done.

I could also draw an acute angle maybe an angle that is formed from an intersection of two lines, so this angle would be acute, and so will this angle.

This angle is different than that angle.

That angle is equal to this angle.

But alternate exterior is that angle and that angle.

And this angle plus that angle plus that angle have to be equal to 180.

You could say that this angle right here angle AB, angle ABE

And so, if this angle is congruent to that angle, that angle is congruent to that angle, then they're congruent to each other

Now, you could do that with mirrors from one angle.

What if we could get at him from that angle?

So, that angle is equal to that angle and that ABD, which is this angle is congruent to DCA which is that angle over here

So, we know from the contradiction that the measure of angle A cannot equal the measure of angle C.

That angle.

That angle

So, that angle must be equal to that angle there

Then we would know that that angle is equal to that angle.

Sure it won't. From that angle, Paris or Nice, same difference.

So, that we know that angle, so, for example angle CAE

And that angle 4 is congruent to angle 3.

But... from a certain angle... yes.

And that angle.

So, we're just saying that this angle is equal to that angle

This angle is going to be congruent to that angle

This angle is congruent to that angle, they're corresponding angles.

So that when you saw from one little angle was like this.

So that angle and that angle would be corresponding angles, so they would be congruent, and then that angle and that angle would be corresponding angles so they'd also be congruent.

Angle BDC over here, it is an alternate interior angle with this angle right over here with that angle right over there

So that is a 90 degree angle, a 90 degree angle and that is a 90 degree angle over there

If that angle is congruent to that angle, something interesting has to happen.

The only way that this would be equal to 180, angle 3 plus angle 4, is if angle 4 were a 90 degree angle, and angle 3 were also a 90 degree angle.

The world looks better from this angle.

So we know that angle CBE and angle so this is CBE and angle DBC are supplementary.

This angle is equal to this vertical angle, is equal to its vertical angle right over here and that this angle is equal to this angle that is opposite the intersection right over here.

If you break it up into triangles, this angle plus that angle plus that angle has to be equal to 180.

So they're saying that angle 2 is congruent to angle 1.

So this angle and that angle have to be the same.

Now this angle corresponds to that angle, but they're not equal.

we know that this is DBA right over here we also know that angle DBA and angle DBC are supplementary this angle and this angle are supplementary, their outer sides form a straight angle, they are adjacent so they are supplementary which tells us that angle DBA, this angle right over here, plus angle DBC, this angle over here, is going to be equal to 180 degrees.

That means that angle 3 plus angle 4 have to be equal to 180.

But when you're the victim, things look a lot differently from that angle.

And you can see from our measure right over here that that gives us a 90 degree angle, which is a very interesting angle that shows up many times in geometry and trigonometry, and there's a special word for a 90 degree angle it is called a right angle.

So that means that this angel, is equal to this angle, is equal to that angle

For example, if you know that angle C is congruent to angle

Let's say if you knew that angle C was congruent to angle