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Giải bài 3.24 trang 44 sách bài tập toán 7 - Kết nối tri thức với cuộc sống

Cho hình 3.24 a)Giải thích tại sao

💜Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Kết nối tri thức

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Đề bài

Cho hình 3.24.

a) Giải thích tại sao \(yy'\parallel zz'\). b) Tính số đo góc ABz. c) Vẽ tia phân giác At của góc MAB, tia At cắt đường thẳng zz’ tại H. Tính số đo góc AHN.

Phương pháp giải - Xem chi tiết

a) Chỉ ra yy’ và zz’ cùng vuông góc với đường thẳng thứ 3 b) -Tính góc ABH -Tính góc ABz (kề bù góc ABH) c) -Tính góc BAM -Tính góc AHB -Tính góc AHN. 

Lời giải chi tiết

a)Ta có: \(\left\{ \begin{array}{l}yy' \bot MN\\zz' \bot MN\end{array} \right. \Rightarrow yy'\parallel zz'\)b)Ta có: \(yy'\parallel zz' \Rightarrow \widehat {xAM} = \widehat {ABN} = {60^0}\) (hai góc đồng vị)Mà \(\widehat {ABz} + \widehat {ABN} = {180^0}\) (2 góc kề bù)\(\begin{array}{l} \Rightarrow \widehat {ABz} + {60^0} = {180^0}\\ \Rightarrow \widehat {ABz} = {180^0} - {60^0}\\ \Rightarrow \widehat {ABz} = {120^0}\end{array}\)c)Ta có: \(yy'\parallel zz' \Rightarrow \widehat {ABz} = \widehat {BAM} = {120^0}\) (2 góc so le trong)Mà tia phân giác At của góc MAB nên \(\widehat {BAH} = \widehat {HAM} = \dfrac{{\widehat {BAM}}}{2} = \dfrac{{{{120}^0}}}{2} = {60^0}\) (Tính chất tia phân giác của góc)\(yy'\parallel zz' \Rightarrow \widehat {HAM} = \widehat {AHB} = {60^0}\) (2 góc so le trong)Mặt khác: \(\widehat {AHB} + \widehat {AHN} = {180^0}\) (2 góc kề bù)\(\begin{array}{l} \Rightarrow {60^0} + \widehat {AHN} = {180^0}\\ \Rightarrow \widehat {AHN} = {180^0} - {60^0}\\ \Rightarrow \widehat {AHN} = {120^0}\end{array}\)

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