Final answer:
Without additional information about points Z and F, statements a and b cannot be confirmed based on the congruency of triangles ABC and DEC. However, statements c and d are true because they follow directly from the congruence of the two triangles.
Step-by-step explanation:
If it's given that triangle ABC is congruent to triangle DEC, we know that their corresponding angles and sides are equal to each other due to the definition of congruent triangles. This means that angle A is equal to angle D, angle B is equal to angle E, and angle C is equal to angle F. Similarly, the side BA is equal to side ED, side AC is equal to side DF, and side BC is equal to side EF.
We can address each of the statements in the question as follows:
- Statement a: ∠ZB = ∠CE. Since we are not given any information about points Z or F, we cannot confirm this statement based on the given congruence.
- Statement b: ∠ZA = ∠CD. Again, point Z is unknown to us, so we cannot confirm this statement based on the information provided.
- Statement c: CD = BA. This statement is true because in congruent triangles corresponding sides are equal; hence CD must be equal to BA.
- Statement d: BE = ED. This statement is true given that triangle DEC is likely an isosceles triangle with BE and ED being the congruent sides.
Based on the information provided, statements c and d are correct statements since they are a direct result of the congruence of triangles ABC and DEC. However, since points Z and F have not been defined in the given triangles, statements a and b are not necessarily true and therefore cannot be confirmed from the given congruency of triangles ABC and DEC.