Question

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

Explanation:

Step1: Identify the common angle

$\angle A\cong\angle A$ (Reflexive property of congruence)

Step2: Use the AA (Angle - Angle) similarity criterion

In $\triangle AED$ and $\triangle ACB$, since $\angle AED\cong\angle ACB$ (given) and $\angle A\cong\angle A$ (common angle), then $\triangle AED\sim\triangle ACB$ (AA similarity criterion)

Step3: Use the property of similar triangles

If $\triangle AED\sim\triangle ACB$, then $\angle ABC\cong\angle ADE$ (Corresponding angles of similar triangles are congruent)

Answer:

$\angle ABC\cong\angle ADE$ is proved as above.