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Giải bài 3 trang 104 SGK Toán 8 tập 1 - Cánh diều

Cho hình chữ nhật ABCD.

ᩚᩚᩚᩚᩚᩚ⁤⁤⁤⁤ᩚ⁤⁤⁤⁤ᩚ⁤⁤⁤⁤ᩚ𒀱ᩚᩚᩚTổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Cánh diều

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

♊Cho hình chữ nhật ABCD. Trên cạnh AB lấy hai điểm M, N sao cho \(AM = NB < \dfrac{1}{2}AB\). Chứng minh tứ giác MNCD là hình thang cân

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Chứng minh MNCD là hình thang có 2 đường chéo bằng nhau

Lời giải chi tiết

ABCD là hình chữ nhật suy ra AD = BCVì: AM = BN suy ra AN = BM \(M,N \in AB\)Mà: AB//CD suy ra MN//CD suy ra MNCD là hình thang.Áp dụng định lí pythagore của \(\Delta AND\) vuông tại A có:\(N{D^2} = A{N^2} + A{D^2} = B{M^2} + B{C^2}\left( 1 \right)\)Áp dụng định lí pythagore của \(\Delta NBC \) vuông tại B có:\(M{C^2} = B{M^2} + B{C^2}\left( 2 \right)\)Từ (1), (2) suy ra: \(M{C^2} = M{D^2} \Rightarrow MC = ND\)Vậy hình thang MNCD có 2 đường chéo MC = ND nên MNCD là hình thang cân.

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