4. l and m are two parallel lines intersected by another pair of parallel lines p and q (see Fig. 7.19). Show that ΔABC ≅ ΔCDA.
Solution: It is given that p || q and l || m To prove: Triangles ABC and CDA are similar i.e. ΔABC ≅ ΔCDA Proof: Consider the ΔABC and ΔCDA, (i) ∠BCA = ∠DAC and ∠BAC = ∠DCA Since they are alternate interior angles (ii) AC = CA as it is the common arm So, by ASA congruency criterion, ΔABC ≅ ΔCDA.
