It is known that △ ABC, ad bisects ∠ BAC and intersects BC with D, DB = DC. Prove that △ ABC is an isosceles triangle. Prove that: ∵ DB = DC ∵ ad is the middle line of △ ABC ∵ ad bisects ∠ BAC and intersects BC with D ∵ ad is also the angle bisector of ∠ BAC in △ ABC. Is ∵ ABC an isosceles triangle?

It is known that △ ABC, ad bisects ∠ BAC and intersects BC with D, DB = DC. Prove that △ ABC is an isosceles triangle. Prove that: ∵ DB = DC ∵ ad is the middle line of △ ABC ∵ ad bisects ∠ BAC and intersects BC with D ∵ ad is also the angle bisector of ∠ BAC in △ ABC. Is ∵ ABC an isosceles triangle?

The middle line and angle bisector can't be proved in this way directly. Without this theorem, the score of the second floor will be deducted in the senior high school entrance examination. The method is wrong and can't be proved congruent directly. I provide the proof method of double length middle line, which our teacher said. We need another proof: extend ad to e to make de = ad connect be ∵ DB = DC, de = ad, ∠ ADC = ∠ BDE ≌ ADC ≌ CDB ≌ AC = be, In this way, ab = AC