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Giải bài 9.42 trang 110 SGK Toán 8 tập 2 - Kết nối tri thức

Cho hình 9.74, biết rằng

💫Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

Cho hình 9.74, biết rằng \(\widehat {AB{\rm{D}}} = \widehat {AC{\rm{E}}}\). Chứng minh rằng ΔABD ∽ ΔACE và ΔBOE ∽ ΔCOD 

 

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Chứng minh ΔBOE  và ΔCOD có: \(\widehat {C{\rm{D}}O} = \widehat {BEO}\) và \(\widehat {EBO} = \widehat {DCO}\)

Lời giải chi tiết

- Xét tam giác ABD và tam giác ACE có \(\widehat {AB{\rm{D}}} = \widehat {AC{\rm{E}}}\), góc A chung

=> ΔABD ∽ ΔACE (g.g)

- Vì ΔABD ∽ ΔACE 

=> \(\widehat {A{\rm{D}}B} = \widehat {A{\rm{E}}C}\) => \(\widehat {C{\rm{D}}O} = \widehat {BEO}\) (1) - Có \(\widehat {AB{\rm{D}}} = \widehat {AC{\rm{E}}}\) Mà \(\widehat {AB{\rm{D}}} + \widehat {EBO} = {180^o}\)       \(\widehat {AC{\rm{E}}} + \widehat {DCO} = {180^o}\) => \(\widehat {EBO} = \widehat {DCO}\) (2)

Từ (1) và (2) => ΔBOE ∽ ΔCOD (g.g)

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Tham Gia Group Dành Cho Lớp 8 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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