\(\left\{{}\begin{matrix}AB=AC\\BM=MC\\AM.chung\end{matrix}\right.\Rightarrow\Delta AMB=\Delta AMC\left(c.c.c\right)\\ \Rightarrow\widehat{AMB}=\widehat{AMC};\widehat{B}=\widehat{C};\widehat{BAM}=\widehat{CAM}\)
Mà \(\widehat{AMB}+\widehat{AMC}=180^0\Rightarrow\widehat{AMB}=\widehat{AMC}=90^0\)
Xét \(\Delta ABC:\widehat{A}+\widehat{B}+\widehat{C}=180^0\)
\(\Rightarrow2\widehat{B}=180^0-\widehat{A}=100^0\\ \Rightarrow\widehat{B}=\widehat{C}=50^0\)
Lại có \(\widehat{BAM}=\widehat{CAM}\Rightarrow\widehat{BAM}=\widehat{CAM}=\dfrac{1}{2}\widehat{BAC}=40^0\)
⎪⎨⎪⎩AB=ACBM=MCAM.chung⇒ΔAMB=ΔAMC(c.c.c)⇒ˆAMB=ˆAMC;ˆB=ˆC;ˆBAM=ˆCAM{AB=ACBM=MCAM.chung⇒ΔAMB=ΔAMC(c.c.c)⇒AMB^=AMC^;B^=C^;BAM^=CAM^
Mà ˆAMB+ˆAMC=1800⇒ˆAMB=ˆAMC=900AMB^+AMC^=1800⇒AMB^=AMC^=900
Xét ΔABC:ˆA+ˆB+ˆC=1800ΔABC:A^+B^+C^=1800
⇒2ˆB=1800−ˆA=1000⇒ˆB=ˆC=500⇒2B^=1800−A^=1000⇒B^=C^=500
Lại có
