Cho tam giác ABC là tam giác nhọn ; có đường cao Ah . Trên nửa mặt phẳng bờ AB chứa điểm C vẽ AF vuông góc với AB và AF = AB
a) Chứng Minh Eb =Fc
b) Chứng Minh N là trung điểm của EF
giải giúp mình mình tick cho nha bạn giải giúp mình nha
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
ΔABD đều
=>AB=AD=BD và \(\hat{BAD}=\hat{ADB}=\hat{ABD}=60^0\)
ΔACE đều
=>AC=CE=AE và \(\hat{CAE}=\hat{ACE}=\hat{AEC}=60^0\)
Ta có: \(\hat{DAC}=\hat{DAB}+\hat{BAC}=60^0+\hat{BAC}\)
\(\hat{BAE}=\hat{BAC}+\hat{CAE}=60^0+\hat{BAC}\)
Do đó: \(\hat{DAC}=\hat{BAE}\)
Xét ΔDAC và ΔBAE có
DA=BA
\(\hat{DAC}=\hat{BAE}\)
AC=AE
Do đó: ΔDAC=ΔBAE
a: Xet ΔAEB và ΔAFC có
góc AEB=góc AFC
góc A chung
=>ΔAEB đồng dạng với ΔAFC
=>AE/AF=AB/AC
=>AE/AB=AF/AC
b: Xét ΔAEF và ΔABC co
AE/AB=AF/AC
góc A chung
=>ΔAEF đồng dạng với ΔABC
a: Ta có: ΔABD đều
=>BA=BD=AD và \(\hat{ABD}=\hat{ADB}=\hat{DAB}=60^0\)
Ta có: ΔAEC đều
=>AE=EC=AC và \(\hat{AEC}=\hat{ACE}=\hat{EAC}=60^0\)
\(\hat{DAC}=\hat{DAB}+\hat{BAC}=60^0+\hat{BAC}\)
\(\hat{BAE}=\hat{BAC}+\hat{EAC}=60^0+\hat{BAC}\)
Do đó: \(\hat{DAC}=\hat{BAE}\)
Xét ΔDAC và ΔBAE có
DA=BA
\(\hat{DAC}=\hat{BAE}\)
AC=AE
Do đó: ΔDAC=ΔBAE
b: ΔDAC=ΔBAE
=>\(\hat{ADC}=\hat{ABE}\)
Xét tứ giác ADBM có \(\hat{ADM}=\hat{ABM}\)
nên ADBM là tứ giác nội tiếp
=>\(\hat{BMD}=\hat{BAD}=60^0\)
\(\hat{BMD}+\hat{BMC}=180^0\) (hai góc kề bù)
=>\(\hat{BMC}=180^0-60^0=120^0\)