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The problem involves triangle \(ABC\), where \(A\) is the vertex of the triangle, and points \(D\) and \(E\) lie on sides \(AC\) and \(AB\) respectively, such that \(AD = AF\). The questions involve proving the following:

a) Proving \( \triangle ADB = \triangle AEC \).
b) Let \( I \) be the intersection of lines \(BD\) and \(CF\). What type of triangle is \(IBC\)? Justify your answer.
c) Prove that \(ED \parallel BC\).

I will go through each of these in detail. Do you want me to start solving them one by one or would you like a broader explanation of the overall approach first?

Cho tam giác ABC cân ở A. Lấy điểm D thuộc cạnh AC và điểm E thuộc cạnh AB sao cho AD = AF. a) Chứng minh ΔADB = ΔAEC. b) Gọi I là giao điểm của BD và CF. Tam giác IBC là tam giác gì? Vì sao? c) Chứng minh ED // BC.

Solve and learn how to prove properties in an isosceles triangle ABC. The problem involves proving triangle congruence (ΔADB = ΔAEC), analyzing the type of triangle (IBC), and proving that line ED is parallel to BC. Suitable for students in Grades 10-12 studying geometric proofs.

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