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H24
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TD
15 tháng 6 2022 lúc 20:31

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JE
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NT
17 tháng 5 2021 lúc 10:35

a) Xét ΔAEB vuông tại E và ΔAFC vuông tại F có 

\(\widehat{FAC}\) chung

Do đó: ΔAEB\(\sim\)ΔAFC(g-g)

Suy ra: \(\dfrac{AE}{AF}=\dfrac{AB}{AC}\)(Các cặp cạnh tương ứng tỉ lệ)

hay \(AE\cdot AC=AF\cdot AB\)(ĐPCM)

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NT
17 tháng 5 2021 lúc 10:36

b)

Ta có: \(\dfrac{AE}{AF}=\dfrac{AB}{AC}\)(cmt)

nên \(\dfrac{AE}{AB}=\dfrac{AF}{AC}\)

Xét ΔAEF và ΔABC có 

\(\dfrac{AE}{AB}=\dfrac{AF}{AC}\)(cmt)

\(\widehat{FAE}\) chung

Do đó: ΔAEF\(\sim\)ΔABC(c-g-c)

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NT
17 tháng 5 2021 lúc 10:41

d) Xét ΔBFC vuông tại F và ΔBDA vuông tại D có 

\(\widehat{FBD}\) chung

Do đó: ΔBFC\(\sim\)ΔBDA(g-g)

Suy ra: \(\dfrac{BF}{BD}=\dfrac{BC}{BA}\)(Các cặp cạnh tương ứng tỉ lệ)

hay \(BF\cdot BA=BD\cdot BC\)

Xét ΔBEC vuông tại E và ΔADC vuông tại D có 

\(\widehat{BCE}\) chung

Do đó: ΔBEC\(\sim\)ΔADC(g-g)

Suy ra: \(\dfrac{CE}{CD}=\dfrac{CB}{CA}\)(Các cặp cạnh tương ứng tỉ lệ)

hay \(CE\cdot CA=CB\cdot CD\)

Ta có: \(BF\cdot BA+CE\cdot CA\)

\(=BC\cdot BD+BC\cdot CD\)

\(=BC\left(BD+CD\right)\)

\(=BC\cdot BC=BC^2\)(Đpcm)

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PB
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CT
12 tháng 9 2017 lúc 6:07

Ta có:  B O C ^ = 2 B A C ^ ,   C O A ^ = 2 C B A ^ ,   A O B ^ = 2 A C B ^

( góc ở tâm gấp 2 lần số đo góc nội tiếp cùng chắn 1 cung )

S = S O A B + S O B C + S O C A  

=  1 2 O A . O B . sin A O B ^ + 1 2 O B . O C . sin B O C ^ + 1 2 O C . O A . sin C O A ^

S = 1 2 R 2 sin 2 A + sin 2 B + sin 2 C  .

ĐÁP ÁN A

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NN
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BX
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BX
17 tháng 5 2023 lúc 22:46

mình cần gâps huhu

 

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NT
17 tháng 5 2023 lúc 22:48

Mở ảnh

=>AM=AN

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PN
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NH
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PB
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CT
10 tháng 3 2017 lúc 11:43

Giải sách bài tập Toán 9 | Giải bài tập Sách bài tập Toán 9

Vì M nằm trong tam giác ABC nên ta có:

Giải sách bài tập Toán 9 | Giải bài tập Sách bài tập Toán 9

Khi đó điểm M nhìn các cạnh AB,BC,CA của tam giác ABC dưới một góc bằng 120 °

Ta có thẻ dựng điểm M như sau:

Dựng cung chứa góc  120 °  vẽ trên đoạn BC

Dựng cung chứa góc  120 °  vẽ trên đoạn AC

Giao điểm thứ hai ngoài C của hai cung này là điểm M cần dựng

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QL
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KT
17 tháng 9 2023 lúc 22:11

a)

Nhận xét: H là một điểm nằm trong tam giác ABC.

b)

Nhận xét: H trùng với đỉnh A của tam giác ABC.

c)

Nhận xét: H nằm ngoài tam giác ABC.

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HD
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