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Giải bài 4 trang 59 sách bài tập toán 8 - Chân trời sáng tạo tập 2

Trong Hình 7, cho biết RV là tia phân giác của góc SRT và UV//RT. Chứng minh rằng:

💧Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Chân trời sáng tạo

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

Trong Hình 7, cho biết RV là tia phân giác của góc SRT và UV//RT. Chứng minh rằng: a) $\Delta SUV\backsim \Delta SRT$. b) \(\frac{{SU}}{{UR}} = \frac{{SR}}{{RT}}\).

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức về định lí về hai tam giác đồng dạng: Nếu một đường thẳng cắt hai cạnh của một tam giác và song song với cạnh còn lại thì nó tạo thành một tam giác mới đồng dạng với tam giác đã cho.

Lời giải chi tiết

a) Tam giác SRT có: UV//RT nên $\Delta SUV\backsim \Delta SRT$b) Vì UV//RT nên \(\widehat {RVU} = \widehat {VRT}\) (hai góc so le trong)Mà \(\widehat {URV} = \widehat {VRT}\) (vì RV là tia phân giác của góc SRT) nên \(\widehat {RVU} = \widehat {URV}\)Do đó, tam giác RUV cân tại U. Suy ra \(UR = UV\).Lại có: $\Delta SUV\backsim \Delta SRT$ nên \(\frac{{SU}}{{SR}} = \frac{{UV}}{{RT}}\). Do đó, \(\frac{{SU}}{{UR}} = \frac{{SR}}{{RT}}\)

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

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