Question

In the following diagram, AD || BC and AB || DC.
Prove angle A is congruent to angle C

Answer 1

They are vertical angles but in a different form.

If AD = BC then AC must be congruent. Transitive Property

Answer 2

Let’s use a two-column proof:

Statement: Reason:

AD || BC Given

∠1 ≅ ∠4. Alternate Interior Angles

Theorem

AB || DC Given

∠2 ≅ ∠3 Alternate Interior Angles

Theorem

━ ━
DB ≅ BD Reflexive Property of

Equality

ΔDAB ≅ ΔDCB ASA Postulate