If CD is a median of ΔABC, then
AD = DB
∠ACD = ∠DCB
CD = AD
∠CAD = ∠CBD
A median of a triangle from any vertex to the opposite side divides it into two equal parts.
So, in ΔABC, if CD is the median, then AD = DB.
Consider Δ ABC. If ADDB=AEEC and ∠ ADE = ∠ ACB. Then Δ ABC is an equilateral triangle.