l and m are two parallel lines intersected by another pair of parallel lines p and q (see the given figure). Show that ΔABC ≅ ΔCDA.

Solution:

In $\triangle \mathrm{ABC}$ and $\triangle \mathrm{CDA}$,

$\angle \mathrm{BAC}=\angle \mathrm{DCA}$ (Alternate interior angles, as $p \| q$ )

$\mathrm{AC}=\mathrm{CA}$ (Common)

$\angle \mathrm{BCA}=\angle \mathrm{DAC}$ (Alternate interior angles, as $/ \| m$ )

$\therefore \triangle \mathrm{ABC} \cong \triangle \mathrm{CDA}(\mathrm{By} \mathrm{ASA}$ congruence rule $)$