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Giải Bài 2 trang 65 sách bài tập toán 7 - CTST

Cho tam giác ABC có M là điểm đồng quy của ba đường phân giác. Qua M vẽ đường thẳng song song với Bc và cắt AB, AC lần lượt tại N và P. Chứng minh rằng NP = BN + CP.

ᩚᩚᩚᩚᩚᩚ⁤⁤⁤⁤ᩚ⁤⁤⁤⁤ᩚ⁤⁤⁤⁤ᩚ𒀱ᩚᩚᩚTổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Chân trời sáng tạo

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

Cho tam giác ABC có M là điểm đồng quy của ba đường phân giác. Qua M vẽ đường thẳng song song với Bc và cắt AB, AC lần lượt tại N và P. Chứng minh rằng  NP = BN + CP.

Phương pháp giải - Xem chi tiết

- Chứng minh MN = BN - Chứng minh MP = CP Suy ra: NP = MN + MP = BN + CP

Lời giải chi tiết

Ta có MN // BC, do đó \(\widehat {{M_1}} = \widehat {{B_1}}\) (so le trong)Dẫn đến \(\widehat {{M_1}} = \widehat {{B_2}}\)(cùng bằng \(\widehat {{B_1}}\)), suy ra tam giác NMB cân tại N nên  MN = BNTa có MP // BC, do đó \(\widehat {{M_2}} = \widehat {{C_2}}\) (so le trong)Dẫn đến \(\widehat {{M_2}} = \widehat {{C_1}}\)(cùng bằng \(\widehat {{C_2}}\)), suy ra tam giác PMC cân tại P nên  MP = CPTa có: NP = MN + MP = BN + CP.

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