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Giải bài 4.26 trang 89 SGK Toán 8 tập 1 - Kết nối tri thức

Cho tam giác ABC,

ꦅTổng 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 tam giác ABC, điểm I thuộc cạnh AB, điểm K thuộc cạnh AC. Kẻ IM song song với BK (M thuộc AC), kẻ KN song song với CI (N thuộc AB). Chứng minh MN song song với BC.

Phương pháp giải - Xem chi tiết

Áp dụng định lí Thalès đảo với IM //BK, KN // CI, ta có các tỉ lệ thức, từ đó ta có tỉ lệ thức để suy ra MN // BC

Lời giải chi tiết

Áp dụng định lí Thalès: • Vì IM // BK nên \(\dfrac{{AI}}{{AB}} = \dfrac{{AM}}{{AK}}\)suy ra AB . AM = AI . AK           (1) • Vì KN // IC nên \(\dfrac{{AN}}{{AI}} = \dfrac{{AK}}{{AC}}\) suy ra AN . AC = AI . AK            (2) Từ (1) và (2) suy ra AB . AM = AN . AC (= AI . AK)         Do đó \(\dfrac{{AN}}{{AB}} = \dfrac{{AM}}{{AC}}\) (theo tính chất tỉ lệ thức). Suy ra MN // BC (theo định lí Thalès đảo).

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