Question

Which congruence theorem would complete the proof shown?

SSS
SAS
ASA

Answer 1

The Angle Side Angle Theorem would complete the proof. It goes from having a congruent angle to the same side (so congruent side) then congruent angle again.

I hope this helps!

Answer 2

In the figure, AB || DC and AC is a transversal.

So, ∠2 = ∠3

∠1 = ∠4 (alternate interior angles)

Now, in triangles ACB and ACD,

∠2 = ∠3

∠1 = ∠4

AC = AC (common)

Therefore, Δ ACB ≅ Δ ACD (ASA Rule)