Prove this triangle as an isosceles triangle when ,there altitudes are equal .Please tell me by taking the triangles ABD and triangle ACE

EC=BD
Angle BEC = angleBCD
BC =BC(common)
By RHS triangle BEC is congurent to triangle CDB
By cpct , angle EBC = angle DCB
AB=AC (as sides opposite to equal sides are equal)
Hence ABC is an isosceles triangle

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