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Giải bài 9.14 trang 71 SGK Toán 7 tập 2 - Kết nối tri thức

Hãy giải thích: Nếu M là một điểm tùy ý nằm trên cạnh BC hoặc cạnh CD của hình vuông ABCD thì độ dài đoạn thẳng AM luôn lớn hơn hoặc bằng độ dài cạnh của hình vuông đó. (H.9.21)

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Đề bài

Hãy giải thích: Nếu M là một điểm tùy ý nằm trên cạnh BC hoặc cạnh CD của hình vuông ABCD thì độ dài đoạn thẳng AM luôn lớn hơn hoặc bằng độ dài cạnh của hình vuông đó. (H.9.21)

Phương pháp giải - Xem chi tiết

Sử dụng định lí: + Trong các đường xiên và đường vuông góc kẻ từ 1 điểm nằm ngoài 1 đường thẳng đến đường thẳng đó thì đường vuông góc là đường ngắn nhất.

Lời giải chi tiết

Vì ABCD là hình vuông nên BC = CD ( tính chất)* Với M nằm trên cạnh BC, ta xét 2 trường hợp sau:+) M khác BAB là đường vuông góc kẻ từ A đến BC; AM là đường xiên kẻ từ A đến BC nên AB < AM ( đường vuông góc luôn nhỏ hơn đường xiên). Do đó, AM lớn hơn độ dài cạnh của hình vuông+) M trùng B:AM = AB. Do đó, AM bằng độ dài cạnh của hình vuôngTrường hợp M nằm trên cạnh CD tương tự.Vậy độ dài đoạn thẳng AM luôn lớn hơn hoặc bằng độ dài cạnh của hình vuông đó.

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