Constructions & proofs
Proofs with congruent triangles
1 / 5Standard
Line segments AB and CD intersect at point O, with AD // CB and OA = OB. The proof that △OAD ≡ △OBC is written as follows:
[Proof]
In △OAD and △OBC,
From the given condition, OA = OB ... (1)
Vertical angles are equal, so ∠AOD = ∠BOC ... (2)
Also, alternate interior angles of parallel lines AD // CB are equal, so ∠OAD = ∠OBC ... (3)
From (1), (2), and (3), since ( ),
△OAD ≡ △OBC.
Which of the following is the most appropriate congruence condition to fill in the blank?