PAIBOTLearn
Sign inSign up

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?