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

 

 

 

 

 

 

 

 

Given: l || m and p || q

To Prove: ΔABC ≅ ΔCDA.

Proof: In ΔABC and ΔCDA,

∠BAC = ∠DCA (Alternate interior angles, as p and q are parallel lines)

AC = CA (Common)

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

∴ ΔABC ≅ ΔCDA (By ASA congruence rule)

Hence, proved.