Question

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

Answer 1

Its given that $l||m$ and $p||q$. We have to prove that $△ABC\cong △CDA$

Taking $l||m$ and $AC$ is the transversal, $\angle ACB=\angle CAD$ [alternate angle]....(i)

Considering $p||q$ and $AC$ is the transversal, $\angle BAC=\angle DCA$ [alternate angles].....(ii)

$\therefore$ In $△ABC$ and $△CDA$,

$\angle ACB=\angle CAD$ [alternate angles]

$AC=AC$ [common base]

$\angle BAC=\angle DCA$ [alternate angles]

$\therefore △ABC\cong △CDA$ [ASA Congruence Rule]