From the given figure, assuming \(\Delta ABE \cong \Delta ACD\)
. Show that
\(△ADE\) and
\(
△ABC\) are similar.
Proof:
Given \(\Delta ABE \cong \Delta ACD\),
Corresponding parts of congruence triangles are congruent.
\(AB = \) - - - - (1)
And \(AE =\)
i.e \(AD =\) - - - - (2)
Dividing (2) by (1)
\(\frac{AD}{AB} = \frac{AE}{AC}\) - - - - (3)
In \(\Delta ADE\) and \(\Delta ABC\),
\(\angle A =\) ()
\(\frac{AD}{AB} = \frac{AE}{AC}\) (from (3))
So, \(\Delta ADE \sim \Delta ABC\) ()
Hence proved.