Total * * * gives four relationships, I don't know what the fifth one is, and the estimated angle AEB is 90, so only three are conditions, and the fourth one is a conclusion. * * * Four propositions:

Proposition 1: Condition ①+②+③, ④ holds;

Proposition 2: Condition ①+②+④, ③ holds;

Proposition 3: Condition 1+3+4, ② holds;

Proposition 4: Condition ②+③+④, ① holds;

Only the fourth one is false, so you can refer to the definition of triangle edge center.

The following proves the proposition 1 (proposition 2 is actually the same as proposition 1) and proposition 3.

Proposition 1 proof: extend the extension line of AE intersection BC to F.

It is easy to prove that △ADE and △FCE are congruent, AE=FE.

Angle AFB= angle 1= angle 2, AB=BF.

An isosceles triangle has three lines connected into a line, with angle 3= angle 4 and angle AEB=90.

Proposition 3 proves that the AE-BC extension line is extended to F.

Angle AFB= angle 1= angle 2, AB=BF.

Angle 3= angle 4, isosceles triangle with three lines in one, AE=FE.

It is easy to prove △ADE congruence △FCE, DE=CE, and the proof is complete.