Question

Answer 1

`a)` 

Có `{:(BM=9),(AM=6):}}=>(BM)/(AM)=9/6=3/2`

`{:(BN=12),(NC=8):}}=>(BN)/(NC)=12/8=3/2`

Xét `Delta BCA` có \(\dfrac{BM}{AM}=\dfrac{BN}{NC}\left(=\dfrac{3}{2}\right)\)

`=>MN////AC` (Thalè đảo)(dpcm)

`b)`

Xét `Delta BMN` và `Delta BAC` có `MN////AC`

`=>Delta BMN∼Delta BAC`(dpcm)

Có \(\dfrac{BM}{AM}=\dfrac{BN}{NC}\left(cmt\right)\Rightarrow\dfrac{BM}{AM+BM}=\dfrac{BN}{NC+BN}\)

Hay `9/(6+9)=(BN)/(BC)

`=>9/15=(BN)/(BC)`

`=>3/5=(BN)/(BC)`

Có `Delta BMN∼Delta BAC(cmt)` 

`=>` \(\dfrac{BM}{BA}=\dfrac{BN}{BC}=\dfrac{MN}{AC}\)(các cạnh tương ứng)

mà `3/5=(BN)/(BC)`

`=>` $\dfrac{BM}{BA}=\dfrac{BN}{BC}=\dfrac{MN}{AC}=\dfrac{3}{5}$