So, they need to be congruent

And obviously if this is congruent to that and that is congruent to that then these two would have to be congruent to each other

These two triangles are going to be congruent

must be congruent to angle BDE and this is the corresponding angles of congruent triangles

It's going be congruent to angle to triangle CAF

So, ABC is going to be congruent to DCB

Alternate interior angles must be congruent

So, these two angles are going to be congruent

you can see ABC is going to be congruent to DCB, angle DCB and you can say by you can say corresponding angles congruent of congruent triangles

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

We have a side in between that's going to be congruent

So, then we have triangle AEC must be congruent to triangle

And so they're congruent, we know that corresponding sides are going to be congruent so we know our statement 5

Well, if two triangles are congruent then all of the corresponding features of the two triangles are going to be congruent

In particular, we know that angle AEB is going to be congruent to angle CEB because they are corresponding angles of congruent triangles

DBC, right over here, angle DBC is going to be congruent to angle

Now, we know that corresponding angles must be congruent

CAE must be congruent to BDE And now we have a transversal

and we know that by corresponding angles congruent of congruent triangles

So, we know that angle ABD is going to be congruent to angle BDC

This side is congruent to that side

angle ACB is congruent to angle DBC

Angle 1 is congruent to angle 4.

They are congruent triangles.

They are congruent triangles.

Well, it tells us all the corresponding angles are going to be congruent

We know that BAF is congruent to CAE

So, for example, we know that angle CDE is going to be congruent to angle BAE

And then, angle FAC is going to be congruent to angle ABD because they're corresponding angles

So, angle DEC must be let me write this down angle DEC must be congruent to angle BAE

ABE is congruent to triangle CBE Once we know that, we know that all the corresponding angles are congruent

So at triangle BAF we now know is going to be congruent Congruent to triangle we start at the white angle go to the orange angle then go to the unlabeled angle

So, we see that if we have opposite angles that are congruent then or if we have a parallelogram then the opposite angles are going to be congruent

So, alternate interior angles must congruent

They're corresponding sides of congruent triangle

The alternate interior angles are congruent

They're congruent and they are supplementary

So, we can write that triangle AMC, AMC is congruent, congruent to triangle BMC, to triangle BMC, by Side Angle Side congruency, Side Angle Side congruency, and so if both, if they are congruent,

So we say 46 mod 12 is congruent to 10.

And then we see that triangle AEC must be congruent to triangle DEB by side angle side

And, they're also going to be the same to these other characters, down here, because these are congruent triangles.

'cause they're corresponding sides of congruent triangles

We've proven that opposite sides are congruent

Now, if we know that two triangles congruent we know that all corresponding sides and angles are congruent

And the only difference between congruent and being equal is that congruent says they can have the same angle measure, but they could be in different directions.