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Giải Bài 34 trang 115 sách bài tập toán 7 tập 1 - Cánh diều

Quan sát Hình 44, biết ME vuông góc với AB tại E và ME, MF lần lượt là tia phân giác của góc AMB và AMC. Vì sao hai đường thẳng MF và AB song song với nhau?

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Đề bài

Quan sát Hình 44, biết ME vuông góc với AB tại E và ME, MF lần lượt là tia phân giác của góc AMB và AMC. Vì sao hai đường thẳng MF và AB song song với nhau?

Phương pháp giải - Xem chi tiết

Chứng minh hai đường thẳng song song bằng cách chứng minh hai góc bằng nhau và chúng ở một trong các vị trí: đồng vị, so le trong, so le ngoài.

Lời giải chi tiết

Do hai góc AME và AMF♋ là hai góc kề nhau nên \(\widehat {EMF} = \widehat {AME} + \widehat {AMF}\).

Ta có ME, MF lần lượt là tia phân giác của góc AMB và AMC nên

\(\widehat {AME} = \dfrac{1}{2}\widehat {AMB};{\rm{ }}\widehat {AMF} = \dfrac{1}{2}\widehat {AMC}\).Mà \(\widehat {AMB} + \widehat {AMC} = 180^\circ \) (hai góc kề bù) nên\(\widehat {EMF} = \widehat {AME} + \widehat {AMF} = \dfrac{1}{2}\left( {\widehat {AMB} + \widehat {AMC}} \right) = \dfrac{1}{2}{\rm{ }}{\rm{. 180}}^\circ {\rm{  =  90}}^\circ \).

Suy ra: \(\widehat {EMF} = \widehat {MEB}\) mà hai góc này ở vị trí so le trong nên MF // AB (Dấu hiệu nhận biết 2 đường thẳng song song)

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