The following must be true on the given scenario:
a.) Angle BAE is congruent to angle CDE.
- The two angles are a pair of alternate interior angles, which is under the theorem of alternating interior angles and properties of a parallelogram formed by the two triangles, must be congruent.
b.) Triangle ABD is congruent to triangle DCA.
- (Reflexive Property) Triangle ABD = Triangle DBA and Triangle DCA = Triangle ACD. It is given that Triangle ACD is the image of triangle DBA after a 180-degree rotation.
c.) Triangle BDA is congruent to triangle CDA.
- (Reflexive Property) Triangle BDA = Triangle DBA and Triangle CDA = Triangle ACD. It is given that Triangle ACD is the image of triangle DBA after a 180-degree rotation.
d.) Segment DA is congruent to segment AD.
- Reflexive Property
