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Giải bài 6 trang 104 vở thực hành Toán 8 tập 2

Cho hình 9.25, biết rằng \(\widehat{AB\text{D}}=\widehat{AC\text{E}}\). Chứng minh rằng ΔABD ∽ ΔACE và ΔBOE ∽ ΔCOD.

🌟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

𒐪Cho hình 9.25, biết rằng \(\widehat{AB\text{D}}=\widehat{AC\text{E}}\). Chứng minh rằng ΔABD ∽ ΔACE và ΔBOE ∽ ΔCOD.

Phương pháp giải - Xem chi tiết

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

Lời giải chi tiết

♚Hai tam giác ABD và ACE có: $\widehat{ABD}=\widehat{ACE}$ (theo giả thiết); góc A chung.

Do đó $\Delta ABD\backsim \Delta ACE$ (g.g).

♎Hai tam giác BOE và COD có: $\widehat{BOE}=\widehat{COD}$ (hai góc đối đỉnh);

🙈$\widehat{OBE}={{180}^{0}}-\widehat{ABD}={{180}^{0}}-\widehat{ACE}=\widehat{OCD}$.

Do đó $\Delta BOE\backsim \Delta COD$ (g.g).

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