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Fill byline proof

I've taken a screen shot from our fill in the blank proof exercises. And I'm going to work it out, essentially, on digital paper. And then we can fill in the blanks on the actual exercise. So they tell us that BC is parallel to DF. The figure is not drawn to scale-- fair enough. Then they tell us that angle CEF is congruent to angle BAC. CEF, so that's this right over here. CEF is congruent to BAC. So it's congruent to that over there. Then they tell us that CFE is congruent to ABC. Angle CFE is congruent to angle ABC. Then they tell us that segment CF is congruent to BC. Then they tell us that BDE is congruent to ACB. So that's that right over there. Then they tell us DE is congruent to AC. And then finally, they tell us that-- let me do that in a different color-- so BED is congruent to BAC. Let me make sure I get it. BED-- so it's this angle right over here-- is congruent to BAC. BAC is this blue one over there, so we already have a marker for that. So I'll write the blue one just like that. So that's that piece of information as well. Now we're ready for the proof. Now whenever you do any proof, it's good to know what you're trying to prove. So let's just cut to the chase and see where this proof actually goes. So in the last statement of the proof, they say triangle BCA is congruent to triangle BCE because-- and we have to figure out why we can say that based on everything that this proof has proven beforehand. But so we're essentially just proving that triangle BCA, which is this triangle right up here-- this is BCA-- that it is congruent to triangle BCE. BCE is this triangle-- this downward-pointing triangle. So this is what we're trying to prove. This is congruent to that right over here. This triangle is congruent to that triangle. So that's important to keep in mind. And all we know about these two triangles is it they share a side in common, which is equal to itself by the reflexive property. But we don't have any other information. We're going to have to figure out whether other sides are congruent or maybe other angles or something else in order to actually make this statement. So let's see what they've done in the proof. So first they make a statement. And we don't need to correct it, but it's good to follow the narrative of their proof. BCA is congruent to BDE because of angle, side, angle. So let's see, we have an angle, side, angle; angle, side, angle. This triple arc corresponds to D here, corresponds to C there. And you see that even over here. The way they wrote it, D is the middle here, and C is the middle there. So they do correspond to each other....