Question

In the adjoining figure, $l$ & $m$ are two parallel lines intersected by another pair of parallel lines $p$ & $q$. Show that $△ABC\cong △CDA$

Answer 1

In the given figure, two lines $l$ and $m$ are parallel to each other and lines $p$ and $q$ are also a pair of parallel lines intersecting each other at $A,B,C$ and $D.AC$ is joined.
To prove :
$△ABC\cong △CDA$
Proof :
In $△ABC$ and $△CDA$
$AC=AC$ (common)
$\angle ACB=\angle CAD$ (Interior alternate angles as $l\parallel m$)
$\angle BAC=\angle ACD$ (Interior alternate angles as $p\parallel q$)
$△ABC\cong △CDA$ (By $ASA$ axiom)