Question

In the given figure, two parallel line l and m are intersected by two parallel lines p and q.
Show that ΔABC ≅ ΔCDA.

Answer 1

Given: In the given figure, two parallel line l and m are intersected by two parallel lines p and q.

To prove: ΔABC ≅ ΔCDA

Proof:
In ΔABC and ΔCDA,

$\angle$BAC = $\angle$DCA (Alternate interior angles, p$\parallel$q)
$\angle$BCA = $\angle$DAC (Alternate interior angles, l$\parallel$m)
AC = CA (Common side)

$\therefore$ By ASA congruence criteria,
ΔABC ≅ ΔCDA