Question

prove \\( \angle a b c \cong \angle a d e \\).

step	statement	reason
2	\\( \angle c a b \cong \angle e a d \\)	reflexive property
3	type of statement

Explanation:

Step1: Use the Angle - Angle (AA) similarity criterion

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. In \(\triangle ABC\) and \(\triangle ADE\), we have \(\angle ADE\cong\angle ACB\) (given) and \(\angle CAB\cong\angle EAD\) (reflexive property).
Since \(\triangle ABC\) and \(\triangle ADE\) are similar (by AA similarity: \(\angle A=\angle A\) (common angle) and \(\angle ADE = \angle ACB\)), corresponding angles of similar triangles are congruent.

Answer:

\(\angle ABC\cong\angle ADE\) (corresponding angles of similar triangles \(\triangle ABC\) and \(\triangle ADE\) are congruent)