Triangle Congruence with Parallel Lines: Proving CDA ≅ ABC

To answer the question, we need to know all four congruence theorems -

SAS, SAA, ASA, SSA

Now let's see what data we can prove from the question -

AB is parallel to DC

And from this it follows that angle BAC equals angle ACD, because these are equal alternate angles,

Also, we have a shared side AC, so we have a shared angle and side.

We could have proven congruence using AB=DC, and then we would have SAA,

but this is not given to us in the options,

so let's look at the fourth congruence theorem - SSA,

for it to work, we need to show another side, BC=AD,

and this is indeed one of the options!

But it's important to remember that the fourth congruence theorem has a condition,

the theorem is valid only if the angle is opposite to the larger of the two sides,

therefore we need to know that ACAC,

and indeed, one of these options exists!

Thus, we can see that there are two things we need,

and therefore answer D is correct!