`#Mon`
`\text{ Qua A kẻ tia Ax // BC}`
`\text{ Kéo dài BD cắt Ax tại N}`
`Xét` `\triangleDBC` `và` `\triangleDMA` `có:`
`\hat{BDC}=\hat{ADM}(\text{ 2 góc đối đỉnh})`
`\hat{DBC}=\hat{DMA}(\text{ 2 góc so le trong})`
`=>\triangleDBC` $\backsim$ `\triangleDMA(g.g)`
`=>\frac{DC}{DA}=\frac{BC}{AM}=2`
`=>AM=\frac{1}{2}BC=BM`
`Xét` `\triangleAIN` `và` `\triangleMIB` `có:`
`\hat{INA}=\hat{IBM}(\text{ 2 góc so le trong; AM//BC})`
`AN=BN(cmt)`
`\hat{ANI}=\hat{MBI}(\text{ so le trong})`
`=>\triangleAIN=\triangleMIB(g.c.g)`
`=>AI=IM(đpcm)`
