Question

l and m are two parallel lines intersected by another pair of parallel lines p and q show that triangle ABC is congruent to triangle CDA

Answer 1

the two parallel lines I and M are bisecting the pair of P and Q , by forming a vertical point or angle. We have to prove that the triangle ABC is similiar to CDA.
ABC=CDA
by taking the measurement of the angle of triangle ABC, we found that it's measure is(anything as suppose) 60°. Now we take the measurement of CBA= 60° itself.
so, ABC=60°, CBA=60°
=ABC=CBA as their measurement is clear to be the same
[proved]

Answer 2

In ΔABC and ΔCDA,

∠BAC = ∠DCA (Alternate interior angles, as p || q)

AC = CA (Common)

∠BCA = ∠DAC (Alternate interior angles, as l || m)

∴ ΔABC ≅ ΔCDA (By ASA congruence rule)