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Giải bài 9.13 trang 69 SGK Toán 7 tập 2 - Kết nối tri thức

Cho tam giác ABC, điểm D nằm giữa B và C. Chứng minh rằng AD nhỏ hơn nửa chu vi tam giác ABC.

🌊Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Kết nối tri thức

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Đề bài

Cho tam giác ABC, điểm D nằm giữa B và C. Chứng minh rằng AD nhỏ hơn nửa chu vi tam giác ABC.

Phương pháp giải - Xem chi tiết

Áp dụng quan hệ giữa ba cạnh của tam giác ABD và tam giác ACD.

Lời giải chi tiết

Áp dụng quan hệ giữa ba cạnh của tam giác ABD, ta có: AD < AB + BDÁp dụng quan hệ giữa ba cạnh của tam giác ACD, ta có: AD < CD + AC\(\Rightarrow AD + AD < AB+BD+CD+AC\)\(\Rightarrow 2AD<AB+BC+AC\) ( vì \(DB+DC=BC\))\(\Rightarrow\) 2AD < Chu vi tam giác ABC hay AD < (Chu vi tam giác ABC) : 2Vậy AD nhỏ hơn nửa chu vi tam giác ABC.

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