In the given figure, two parallel line l and m are intersected by two parallel lines p and q.

Given: In the given figure, two parallel line l and m are intersected by two parallel lines p and q.

To prove: ΔABC ≅ ΔCDA

Proof:
In ΔABC and ΔCDA,

∠">∠∠BAC = ∠">∠∠DCA           (Alternate interior angles, p∥">∥∥q)
∠">∠∠BCA = ∠">∠∠DAC           (Alternate interior angles, l∥">∥∥m)
AC = CA                        (Common side)

∴">∴∴ By ASA congruence criteria,
ΔABC ≅ ΔCDA