2025 MGS(S) PRELIMS P1 Q26

In the diagram, \(D\) and \(E\) are points on \(BC\) such that \(BD=DC=AC\). Triangle \(ADE\) is congruent to triangle \(FCE\), and angle \(ADE=\theta\).

Show that triangle \(ABD\) is congruent to triangle \(FAC\). Give a reason for each statement you make.[3]