l and m are two parallel lines intersected by another pair of parallel lines p and q(see Fig. 7.19). Show that Δ ABC ≅Δ CDA.

It is given in the figure given, 

l parallel to m

And, p parallel to q

To prove:- ΔABC ≅ ΔCDA  

∠BCA = ∠DAC (Alternate interior angles)

∠BAC = ∠DCA (Alternate interior angles)

And, side AC is common 

Therefore, By ASA congruence,

ΔABC ≅ ΔCDA