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Giải bài 3 trang 77 sách bài tập toán 10 - Chân trời sáng tạo

Trong các phát biểu sau, phát biểu nào đúng?

ౠTổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Trong tam giác ABC có \(A\left( { - 1;1} \right),B\left( {1;3} \right),C\left( {1; - 1} \right)\). Trong các phát biểu sau, phát biểu nào đúng? A. ABC là tam giác có ba cạnh bằng nhau B. ABC là tam giác có ba góc đều nhọn C. ABC là tam giác cân tại B (BA = BC) D. ABC là tam giác vuông cân tại A

Phương pháp giải - Xem chi tiết

Tính các vectơ \(\overrightarrow {AB} ,\overrightarrow {AC} ,\overrightarrow {BC} \) và tìm ra tính chất của tam giác ABC

Lời giải chi tiết

Ta có: \(\overrightarrow {AB}  = \left( {2;2} \right),\overrightarrow {AC}  = \left( {2; - 2} \right),\overrightarrow {BC}  = \left( {0; - 4} \right)\)+ \(AB = AC = 2\sqrt 2 ,BC = 4\) hay tam giác ABC cân tại A (1)=> Loại A, C.+ \(\overrightarrow {AB} .\overrightarrow {AC}  = 2.2 + 2.( - 2) = 0 \Rightarrow AB \bot AC\) => Tam giác ABC vuông tại A (2)=> Loại B.Từ (1) và (2) suy ra ABC là tam giác vuong cân tại AChọn D.

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