Cho tam giác ABC có góc B tù. Chứng minh rằng các góc A và C nhọn.
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CM
Cao Minh Tâm
17 tháng 12 2019
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PT
1
CM
25 tháng 3 2017
Do B tù nên ta có góc ngoài của đỉnh B là góc nhọn, suy ra các góc A, C nhọn.
NP
2
29 tháng 7 2017
vì góc C tù nên góc C lớn hơn 90 độ
Nên góc A, B chỉ có thể là góc nhọn, không thể là góc vuông vì một tam giác có tổng là 180 độ
kbn nha
29 tháng 7 2017
Tam giác ABC có:
\(\widehat{A}+\widehat{B}+\widehat{C}=180\)
Mà \(\widehat{C}\)> 90
\(\Rightarrow\widehat{A}+\widehat{B}< 90\)
\(\Rightarrow\widehat{A}< 90;\widehat{B}< 90\)
11 tháng 11 2019
Xét \(\Delta ABC\)có :
\(\widehat{A}+\widehat{B}+\widehat{C}=180^o\)( định lí tổng 3 góc trong 1 tam giác )
Mà \(\widehat{B}>90^o\)
\(\Rightarrow\widehat{A}+\widehat{C}< 90^o\)
\(\Rightarrow\widehat{A}< 90^0,\widehat{B}< 90^o\)
11 tháng 11 2019
Cho mình sửa lại :
Đoạn cuối :
\(\Rightarrow\widehat{A}< 90^0,\widehat{C}< 90^o\)
NL
Nguyễn Lê Phước Thịnh
CTVHS
2 tháng 3 2022
Bài 2:
Xét ΔABC có \(\widehat{A}>\widehat{B}>\widehat{C}\)
nên BC>AC>AB
15 tháng 6 2022
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
NL
Nguyễn Lê Phước Thịnh
CTVHS
28 tháng 7
a; Xét ΔAEB vuông tại E và ΔAFC vuông tại F có
\(\hat{EAB}\) chung
Do đó:ΔAEB~ΔAFC
=>\(\frac{AE}{AF}=\frac{AB}{AC}\)
=>\(\frac{AE}{AB}=\frac{AF}{AC}\)
=>\(AE\cdot AC=AF\cdot AB\)
b: Xét ΔAEF và ΔABC có
\(\frac{AE}{AB}=\frac{AF}{AC}\)
góc EAF chung
Do đó: ΔAEF~ΔABC
c: Xét ΔAEB vuông tại E có cos EAB=\(\frac{AE}{AB}\)
=>\(\frac{AE}{AB}=cos60=\frac12\)
ΔAEF~ΔABC
=>\(\frac{S_{AEF}}{S_{ABC}}=\left(\frac{AE}{AB}\right)^2=\left(\frac12\right)^2=\frac14\)
=>\(S_{ABC}=4\cdot S_{AEF}\)