Question

$l$ and $m$ are two parallel lines intersected by another pair of parallel lines $p$ and $q$ (see the given figure). Show that $△ABC\cong △CDA$.

Answer 1

Given:

$l\parallel m$ and $p\parallel q$

These pair of parallel lines intersected at $A,B,C$ and $D$ respectively.

To prove: $△ABC\cong △CDA$

Proof:

In $△ABC$ and $△CDA$,

$\angle BAC=\angle DCA$ [Alternate interior angles, as $p\parallel q$]

$AC=CA$ [Common side]

$\angle BCA=\angle DAC$ [Alternate interior angles, as $l\parallel m$]

Therefore, By, $A.S.A$ congruence rule

$△ABC\cong △CDA$

Hence, proved.