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Giải bài 9 trang 41 Chuyên đề học tập Toán 11 Chân trời sáng tạo

Cho tam giác ABC. Vẽ về phía ngoài của tam giác các hình vuông ABEF, ACMN. Chứng minh BN bằng và vuông góc với FC.

♛Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Cho tam giác ABC. Vẽ về phía ngoài của tam giác các hình vuông ABEF, ACMN. Chứng minh BN bằng và vuông góc với FC.

Phương pháp giải - Xem chi tiết

Dựa vào phép quay góc 900để chứng minh BN bằng và vuông góc với FC.

Lời giải chi tiết

Vì ABEF là hình vuông nên AF = AB và \({\rm{(AF,AB)  =  }}\widehat {{\rm{FAB}}}{\rm{ =  }}{90^o}\)Suy ra phép quay tâm A, góc quay 90° biến điểm F thành điểm B (1)Vì ACMN là hình vuông nên AC = AN và \({\rm{(AC,AN)  =  }}\widehat {CAN}{\rm{ =  }}{90^o}\)Suy ra phép quay tâm A, góc quay 90° biến điểm C thành điểm N (2)Từ (1), (2), ta thu được phép quay tâm A, góc quay 90° biến đoạn thẳng FC thành đoạn thẳng BN.Do đó \(FC{\rm{ }} = {\rm{ }}BN\) và \(\left( {FC,{\rm{ }}BN} \right){\rm{ }} = {\rm{ }}90^\circ .\)Vậy \(FC{\rm{ }} = {\rm{ }}BN\)  và \(FC \bot BN.\)

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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