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Answer :
From figure, we have,
\(\angle{1}\) = \(\angle{2}\) (Vertically opposite angles) ...(i)
\(\angle{1}\) = \(\angle{6}\) (Corresponding angles) ...(ii)
\(\angle{6}\) = \(\angle{4}\) (Corresponding angles) ...(iii)
From Equations, (i), (ii) and (iii), we have
\(\angle{1}\) = \(\angle{4}\) and \(\angle{2}\) = \(\angle{6}\) ...(iv)
In \(\triangle{ABC}\) and \(\triangle{CDA}\), we have
\(\angle{4}\) = \(\angle{2}\) ...(from (iii) and (iv))
\(\angle{5}\) = \(\angle{3}\) ...(Alternate angles)
and AC is a common side.
Therefore, we get,
\(\triangle{ABC}\) \(\displaystyle \cong \) \(\triangle{CDA}\) ...(By SAS congruency test)
Hence, proved.