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In the given figure, the problem states the following conditions:

- \( AB = AD \)
- \( AC = AE \)
- \( \angle BAD = \angle EAC \)

From this information, we can make some geometric inferences:

1. Triangles \( \triangle ABD \) and \( \triangle EAC \) are likely isosceles since two sides of each triangle are equal (as given).
2. Additionally, because the angles \( \angle BAD \) and \( \angle EAC \) are equal, we can deduce that triangles \( \triangle ABD \) and \( \triangle EAC \) may be congruent by the **SAS (Side-Angle-Side)** criterion.
   
Hence, congruence or certain relationships between these triangles may help determine which statements are true.

Would you like a more detailed analysis of the options, or do you need further clarification? Let me know!

Here are five related questions to expand this concept:
1. How do we prove triangles are congruent using the SAS criterion?
2. What can be inferred from equal angles and sides in isosceles triangles?
3. How does congruence of triangles help determine relationships between other angles or sides?
4. What other properties can be derived from the figure based on symmetry?
5. How can we apply the concept of cyclic quadrilaterals to problems involving diagonals like in the figure?

**Tip:** When working with congruent triangles, always check if side lengths and angles satisfy congruence criteria like SAS, SSS, or ASA.

In the given figure, AB = AD, AC = AE, and ∠BAD = ∠EAC, then which of the following is true?

Explore the solution to a geometry problem where AB = AD, AC = AE, and ∠BAD = ∠EAC. Learn how to apply triangle congruence theorems like SAS, and discover properties of isosceles triangles. Suitable for students in Grades 9-10.

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