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The math proof problem in junior high school is very simple and needs steps.
Proof: extend AD to BC in H.

∫∠ 1 =∠2,∴bd=cd;

Ⅷ in △ABD and △ACD

AB=AC

AD=AD

BD=CD

∴△ABD≌△ACD(SSS)

∴∠BAD=∠CAD,∠ABD=∠ACD

∠∠BDH =∠ =∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠8736

∴∠BDH=∠CDH

So at △BDH and △CDH,

∠ 1=∠2

∠BDH=∠CDH

DH=DH

So △ BDH △ CDH (AAS)

So BH=CH, ∠ AHB = ∠ AHC = 90.

Therefore, BC was divided vertically in AD.