Bài 2:
Ta có: \(\dfrac{AB}{BD}=\dfrac{9}{12}=\dfrac{3}{4}.\\ \dfrac{BD}{DC}=\dfrac{12}{16}=\dfrac{3}{4}.\)
\(\Rightarrow\dfrac{AB}{BD}=\dfrac{BD}{DC}\left(=\dfrac{3}{4}\right).\)
Xét \(\Delta ABD\) và \(\Delta BDC:\)
\(\widehat{ABD}=\widehat{BDC}\left(AB//DC\right).\)
\(\dfrac{AB}{BD}=\dfrac{BD}{DC}\left(cmt\right).\)
\(\Rightarrow\) \(\Delta ABD\sim\Delta BDC\left(c-g-c\right).\)
Bài 3:
Xét \(\Delta ABC:\)
\(\dfrac{AN}{AB}=\dfrac{AM}{AC}\left(do\dfrac{8}{12}=\dfrac{10}{15}\right).\\ \Rightarrow MN//BC\left(Talet\right).\)
\(\Rightarrow\dfrac{MN}{BC}=\dfrac{AN}{AB}\left(HqTalet\right).\)
\(\Rightarrow\dfrac{MN}{18}=\dfrac{8}{12}.\\ \Rightarrow MN=12\left(cm\right).\)
Bài 4:
Xét \(\Delta ABI\) và \(\Delta DIC:\)
\(\dfrac{AB}{DI}=\dfrac{AI}{DC}\left(AB.DC=AI.DI\right).\\ \widehat{A}=\widehat{D}\left(gt\right).\\ \Rightarrow\Delta ABI\sim\Delta DIC\left(c-g-c\right).\)
Bài 1:
Xét ΔOAD và ΔOBC có
OA/OB=OD/OC
\(\widehat{O}\) chung
Do đó: ΔOAD\(\sim\)ΔOBC
