a.
Xét \(\Delta AMB\) và \(\Delta CMD\) có :
\(MA=MC\left(gt\right)\\ \widehat{AMB}=\widehat{DMC}\left(đ^2\right)\\ MB=MD\left(gt\right)\\ \Rightarrow\Delta AMB=\Delta DMC\left(c-g-c\right)\\ \Rightarrow AB=CD;\widehat{BAC}=\widehat{DCA}\)
Xét \(\Delta ABC\) và \(\Delta DCA\) có :
\(AB=CD\left(cmt\right)\\ \widehat{BAC}=\widehat{DCA}\left(cmt\right)\\ AC\left(chung\right)\\ \Rightarrow\Delta ABC=\Delta CDA\left(c-g-c\right)\)
b.
Xét \(\Delta AFB\) và \(\Delta CED\) có :
\(AB=CD\left(cmt\right)\\ BF=DE\left(gt\right)\\ \Rightarrow\Delta ABF=\Delta CDE\left(ch-cgv\right)\\ \Rightarrow\widehat{AFB}=\widehat{CED}=90^0\\ \Rightarrow AF\perp BC\)
c.
Xét \(\Delta BMF;\Delta DME\) có :
\(MB=MD\left(gt\right)\\ \widehat{MBF}=\widehat{MDE}\\ BF=DE\left(gt\right)\\ \Rightarrow\Delta BMF=\Delta DME\left(c-g-c\right)\\ \Rightarrow\widehat{BMF}=\widehat{DME}\\ \Rightarrow\widehat{DME}+\widehat{DMF}=\widehat{BMF}+\widehat{DMF}\\ \Rightarrow\widehat{MEF}=180^0\)
=> M;E;F thẳng hàng
