As shown in the figure, D is a point inside the triangle ABC, connecting BD and ad, taking BC as the edge, making an angle outside the triangle ABC, CBE = angle abd, BCE = angle bad, be, CE intersecting at point E, connecting de. prove that the triangle DBE is similar to the triangle ABC

As shown in the figure, D is a point inside the triangle ABC, connecting BD and ad, taking BC as the edge, making an angle outside the triangle ABC, CBE = angle abd, BCE = angle bad, be, CE intersecting at point E, connecting de. prove that the triangle DBE is similar to the triangle ABC

Since angle abd = angle CBE, angle bad = angle BCE
So the triangle abd is similar to the triangle bed
So be / BC = BD / BA
There are also angles ABC = angle abd + angle DBC
=Angle DBC + angle CBE
=Angle DBE
So triangle DBE and triangle ABC satisfy that the two corresponding sides are proportional and the angles between them are equal
So the two triangles are similar