初二 数学 急急急
3个回答
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解:
画延长线,延长AM至E,使MD = ME,连接CE,标注∠ACB为∠5,∠DCE为∠6;
∵CM⊥且平分DE,
∴CD = CE
∴∠4 = ∠E
∵AB = AD,
∴∠B = ∠3
又∵∠3 = ∠4,
∴∠3 = ∠4 = ∠B = ∠E
∵∠1+∠B+∠3 = 180°,∠4+∠E+∠6=180°;
∴∠1 = ∠6
∵AD平分∠BAC,
∴∠1 = ∠2
∴∠2 = ∠6
∵∠4 = ∠2+∠5,∠4=∠E,∠2=∠6,
∴∠E = ∠4 = ∠5+∠6 = ∠ACE
∴AE = AC
∵AB = AD,MD = ME,AE = AC,
∴AB+AC = AD+AE = 2(AD+MD)=2AM
∴AM = 1/2(AB+AC)
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