① This topic examines the judgment of isosceles triangle, the nature of congruent triangles and the application of knowledge points such as judgment. The key to solve this problem is to make auxiliary lines correctly, which is also a difficult point. The idea of solving the problem is to put BC and CD in a triangle and prove it according to the judgment of isosceles triangle;

② Intercept AE=AA at AB side, connect CE, and prove △ ACD △ ACE according to SAS (theorem for proving triangle congruence in mathematics: if two sides in two triangles are equal in correspondence and the included angles of the two sides are equal), and deduce CD=CE, ∠ADC=∠AEC, and find out.

explain

Prove:

AB trimming AE=AD, then CE, as shown in the figure.

The picture is a little crooked, sorry. . .

Dyskinesia of communication

∴∠DAC=∠BAC

In △DAC and △EAC.

AD=AE

{∠DAC=∠EAC

Communication = communication

∴△DAC≌△EAC(SAS)

∴CD=CE,∠D=∠AEC

∠∠D+∠B = 180，∠AEC+∠BEC= 180

That is, ∠ AEC+∠ B = 180, and ∠ AEC+∠ BEC = 180.

∴∠B=∠BEC

∴BC=CE

So BC=CD.