Final Answer:
The given information states that AB is parallel to DC, and ABDC is a quadrilateral. Therefore, we can conclude that triangles AABE and ACDE are similar.
Step-by-step explanation:
In the given statement, AB || DC signifies that line AB is parallel to line DC. Additionally, the fact that ABDC is a quadrilateral implies that angle ABE is supplementary to angle CDE, as they are opposite angles in a quadrilateral. When two lines are parallel, corresponding angles are equal. Hence, angle ABE is equal to angle CDE.
Now, considering the triangles AABE and ACDE, they share the angle ABE (which is equal to CDE). To establish similarity between the triangles, we need another pair of corresponding angles to be equal. Since AB is parallel to DC, angle AAB is corresponding to angle CAD, making the two triangles similar by Angle-Angle (AA) similarity.
In summary, due to the parallelism of AB and DC, and the fact that ABDC is a quadrilateral, we can conclude that triangles AABE and ACDE are similar by Angle-Angle similarity. This relationship allows us to affirm that the given statement is valid.