`#Mon`
`a)Xét` `\triangleADB` `và` `triangleADC` `có:`
`\text{ AD là cạnh chung}`
`\text{ AB=AC( do ΔABC cân tại A)}`
`\text{ DB = DC ( do ΔDBC đều)}`
`=>\triangleADB=\triangleADC(c.c.c)`
`=>\hat{DAB}=\hat{DAC}`
`=>\text{ AD là phân giác của}` `\hat{BAC}`
`b)\triangleABC` `có:`
`\hat{A}=20^o`
`\hat{B}=\hat{C}` `\text{ (do ΔABC cân ở A)}`
`Mà` `\hat{A}+\hat{B}+\hat{C}=180^o`
`=->\hat{B}=\hat{C}=\frac{180^o-20^o}{2}=80^o`
`\triangleDBC` `đều` `nên` `\hat{DBC}=\hat{DCB}=\hat{BDC}=60^o`
`=>\hat{DBA}=\hat{ABC}-\hat{DBC}80^o-60^o=20^o=\hat{A}`
`\hat{ABM}=\frac{1}{2}\hat{ABD}=\frac{1}{2}.20^o=10^o`
`\hat{DAB}=\frac{1}{2}\hat{A}=\frac{1}{2}.20^o=10^o`
`Xét` `\triangleMAB` `và` `\triangleDBA` `có:`
`\hat{MAB}=\hat{DBA}=20^o`
`\text{ AB là cạnh chung}`
`\hat{MBA}=\hat{DAB}=10^o`
`=>\triangleMAB=\triangleDBA(g.c.g)`
`=>MA=DB`
`\text{ Mà DB=BC ( do ΔDBC đều)}`
`=>MA=BC(đpcm)`
