According to the condition, if the triangle ADC and BDC are equal, then the angle ADC and BDC are equal.

If AD=BD, the edges and corners prove that the triangle ADE ADE and BDE are equal, and AE=BE, that is, DE is the center line of the isosceles triangle, so it is vertical.

See this topic should be equilateral triangle paper, otherwise it can't be done.

AB=√3, then DE = 3/2, CE = √ 3/2, CD = 3/2-√ 3/2 = 0.63397 (I really don't know how to write this accurately to 0.0 1 ...).