Question

$l$ and $m$ are two parallel lines intersect by another pair of parallel lines $p$ and $q$. Show that $\Delta ABC\cong \Delta CDA$

Answer 1

In $△ABCand△CDA$,

$\angle BCA=\angle DAC$ ------ Alternate interior angles as $p\parallel q$

$AC=CA$ ------ Common side

$\angle BAC=\angle DCA$ ------ Alternate interior angles as $l\parallel m$

Hence, $△ABC\cong △CDA$ (by $ASA$ congruence rule)