Question

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

Answer 1

Given:- $l\parallel mp\parallel q$

To prove:- $△ABC\cong △CDA$

Proof:-

Taking $l\parallel m$ and $AC$ is transversal,

$\angle ACB=\angle CAD\left(\text{Alternate angles}\right)$

Again taking $p\parallel q$ and $AC$ is transversal,

$\angle BAC=\angle DCA\left(\text{Alternate angles}\right)$

Now, in $△ABC$ and $△CDA$,

$\angle ACB=\angle CAD$

$AC=CA\left(\text{Common}\right)$

$\angle BAC=\angle DCA$

$\therefore △ABC\cong △CDA\left(\text{By ASA congruent}\right)$

Hence, proved