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Giải bài 4.42 trang 67 sách bài tập toán 10 - Kết nối tri thức với cuộc sống

Cho hình thoi ABCD có độ dài các cạnh bằng 1

𓄧Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Kết nối tri thức

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Đề bài

Cho hình thoi \(ABCD\) có độ dài các cạnh bằng 1 và \(\widehat {DAB} = {120^ \circ }.\) Khẳng định nào sau đây là đúng? A. \(\overrightarrow {AB}  = \overrightarrow {CD} \) B. \(\overrightarrow {BD}  = \overrightarrow {AC} \) C. \(\left| {\overrightarrow {BD} } \right| = 1\) D. \(\left| {\overrightarrow {AC} } \right| = 1\)

Phương pháp giải - Xem chi tiết

Chứng minh tam giác ABC đều

Lời giải chi tiết

Xét hình thoi có: \(\widehat {DAB} = {120^ \circ }.\)\( \Rightarrow \) \(\widehat {BAC} = \widehat {DAC} = {60^ \circ }\) (t/c)Xét \(\Delta ABC\) có: \(BA = BC\)\( \Rightarrow \) \(\Delta ABC\) cân tại \(B\)Mặt khác \(\widehat {BAC} = {60^ \circ }\)Nên \(\Delta ABC\) là tam giác đều\( \Rightarrow \) \(AC = 1\) hay \(\left| {\overrightarrow {AC} } \right| = 1\)Chọn D.

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