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tu ve hinh :
a, AE | AB va AD | AC (gt) => goc DAC = goc BAE = 90 (dn)
goc DAB + goc BAC = goc DAC
goc EAC + goc CAB = goc BAE
=> goc DAB = goc CAE
xet tamgiac BDA va tamgiac ECA co :
AD = AC (gt) va AB = AE (gt)
=> tamgiac BDA = tamgiac ECA (c - g - c)
=> BD = CE (dn)
Bạn tự vẽ hình nha!!!
a.)Xét\(\Delta ABD\)và\(\Delta ABM\)có:
\(AD=BM\)
\(AB:\)Chung
\(\widehat{DAB}=\widehat{ABM}\left(slt\right)\)
\(\Rightarrow\Delta ABD=\Delta BAM\)
b.)Ta có:\(\Delta ABD=\Delta BAM\)(Theo a)
\(\Rightarrow\widehat{DBA}=\widehat{BAM}\)(mà 2 góc SLT)
\(\Rightarrow AM//BD\)
c.)Xét\(\Delta ADI\)và\(\Delta IMC\)có:
\(AD=CM\)
\(\widehat{DAI}=\widehat{IMC}\)
\(AI=IM\)
\(\Rightarrow\Delta AID=\Delta IMC\)
\(\Rightarrow IA=IC\)
\(\Rightarrow I\)là trung điểm của\(AC\)
\(\Rightarrow I,A,C\)thẳng hàng(đpcm)
P/s:#Study well#
- A là một điểm trên đường thẳng mnm n𝑚𝑛.
- Các tia Abcap A b𝐴𝑏và Adcap A d𝐴𝑑nằm trên cùng một nửa mặt phẳng bờ mnm n𝑚𝑛.
- bAd̂=90∘modified b cap A d with hat above equals 90 raised to the composed with power𝑏𝐴𝑑=90∘.
- bAm̂=2dAn̂modified b cap A m with hat above equals 2 modified d cap A n with hat above𝑏𝐴𝑚=2𝑑𝐴𝑛.
Ta cần tìm số đo của góc dAn̂modified d cap A n with hat above𝑑𝐴𝑛. Step 2: Thiết lập phương trình Vì tia Adcap A d𝐴𝑑nằm giữa hai tia Amcap A m𝐴𝑚và Abcap A b𝐴𝑏, ta có: mAd̂+dAb̂=mAb̂modified m cap A d with hat above plus modified d cap A b with hat above equals modified m cap A b with hat above𝑚𝐴𝑑+𝑑𝐴𝑏=𝑚𝐴𝑏 mAd̂+90∘=mAb̂modified m cap A d with hat above plus 90 raised to the composed with power equals modified m cap A b with hat above𝑚𝐴𝑑+90∘=𝑚𝐴𝑏 Vì tia Ancap A n𝐴𝑛và Amcap A m𝐴𝑚là hai tia đối nhau, ta có: mAd̂+dAn̂=180∘modified m cap A d with hat above plus modified d cap A n with hat above equals 180 raised to the composed with power𝑚𝐴𝑑+𝑑𝐴𝑛=180∘ Từ đó, ta có: mAd̂=180∘−dAn̂modified m cap A d with hat above equals 180 raised to the composed with power minus modified d cap A n with hat above𝑚𝐴𝑑=180∘−𝑑𝐴𝑛 Thay mAd̂modified m cap A d with hat above𝑚𝐴𝑑vào phương trình đầu tiên: (180∘−dAn̂)+90∘=mAb̂open paren 180 raised to the composed with power minus modified d cap A n with hat above close paren plus 90 raised to the composed with power equals modified m cap A b with hat above(180∘−𝑑𝐴𝑛)+90∘=𝑚𝐴𝑏 270∘−dAn̂=mAb̂270 raised to the composed with power minus modified d cap A n with hat above equals modified m cap A b with hat above270∘−𝑑𝐴𝑛=𝑚𝐴𝑏 Theo đề bài, bAm̂=2dAn̂modified b cap A m with hat above equals 2 modified d cap A n with hat above𝑏𝐴𝑚=2𝑑𝐴𝑛. 270∘−dAn̂=2dAn̂270 raised to the composed with power minus modified d cap A n with hat above equals 2 modified d cap A n with hat above270∘−𝑑𝐴𝑛=2𝑑𝐴𝑛 Step 3: Giải phương trình 270∘=2dAn̂+dAn̂270 raised to the composed with power equals 2 modified d cap A n with hat above plus modified d cap A n with hat above270∘=2𝑑𝐴𝑛+𝑑𝐴𝑛 270∘=3dAn̂270 raised to the composed with power equals 3 modified d cap A n with hat above270∘=3𝑑𝐴𝑛 dAn̂=270∘3modified d cap A n with hat above equals the fraction with numerator 270 raised to the composed with power and denominator 3 end-fraction𝑑𝐴𝑛=270∘3 dAn̂=90∘modified d cap A n with hat above equals 90 raised to the composed with power𝑑𝐴𝑛=90∘ Số đo của góc dAn̂modified d cap A n with hat above𝑑𝐴𝑛là 90∘90 raised to the composed with power𝟗𝟎∘.tóm lại là 90 độ
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