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Giải bài 9.36 trang 84 SGK Toán 7 tập 2 - Kết nối tri thức

Cho tam giác ABC có

𒅌Tổng hợp đề thi học kì 2 lớp 7 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 có \(\widehat {BAC}\) là góc tù. Lấy điểm D nằm giữa A và B, lấy điểm E nằm giữa A và C (H.9.51). Chứng minh DE < BC.

Phương pháp giải - Xem chi tiết

-Sử dụng tính chất bắc cầu -Chứng minh DE < DC -Chứng minh DC < BC

Lời giải chi tiết

Ta có \(\widehat {BAC}\)  là góc tù nên \(\widehat {ADE},\widehat {AED}\)  là các góc nhọn\( \Rightarrow \widehat {DEC}\) là góc tù\( \Rightarrow DE < DC\) (quan hệ giữa góc và cạnh đối diện trong tam giác DEC). (1) Xét tam giác ADC có:\(\widehat {DAC}\) là góc tù nên \(\widehat {ADC},\widehat {ACD}\) là các góc nhọn\( \Rightarrow \widehat {BDC}\) là góc tù.\( \Rightarrow DC < BC\) (quan hệ giữa góc và cạnh đối diện trong tam giác BDC) (2)Từ (1) và (2) suy ra: BC > DE

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