Question

prove: \\( \angle a b c \cong \angle a d e \\).
note: quadrilateral properties are not permitted in this proof

step
1
2
3

statement
\\( \angle a e d \cong \angle a c b \\)
\\( \angle c a b \cong \angle e a d \\)
\\( \angle b \cong \angle b \\)
\\( \angle \square \cong \angle \square \\)

reason
given
reflexive property
reflexive property
select a reason...

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 \(\angle AED\cong\angle ACB\) (given) and \(\angle CAB\cong\angle EAD\) (reflexive property). So, \(\triangle ABC\sim\triangle ADE\) by the AA similarity criterion.

Step2: Use the property of similar triangles

If two triangles are similar, then their corresponding angles are congruent. Since \(\triangle ABC\sim\triangle ADE\), the corresponding angles \(\angle ABC\) and \(\angle ADE\) are congruent.

Answer:

\(\angle ABC\cong\angle ADE\) by the AA similarity criterion (for triangles) and the property of similar triangles (corresponding angles of similar triangles are congruent).