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Giải bài 4.42 trang 71 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Cho hình lăng trụ tứ giác ABCD.A’B’C’D’. Gọi O là giao điểm của AC và BD.

🏅Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Kết nối tri thức

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

Cho hình lăng trụ tứ giác ABCD.A’B’C’D’. Gọi O là giao điểm của AC và BD. Gọi O’ là hình chiếu của O qua phép chiếu song song lên mặt phẳng (A’B’C’D’) theo phương AA’. Chứng minh rằng O’ là giao điểm của A’C’ và B’D’.

Phương pháp giải - Xem chi tiết

Phép chiếu song song biến ba điểm thẳng hàng thành ba điểm thẳng hàng và không làm thay đổi thứ tự ba điểm đó.

Lời giải chi tiết

Qua phép chiếu lên mặt phẳng (A’B’C’D’) theo phương AA’, các điểm A, B, C, D, O lần lượt có hình chiếu là A’, B’, C’, D’, O’. Vì phép chiếu song song bảo toàn tính thẳng hàng của các điểm và O nằm giữa A và C nên O’ nằm giữa A’ và C’; Vì phép chiếu song song bảo toàn tính thẳng hàng của các điểm và O nằm giữa B và D nên O’ nằm giữa B’ và D’. Vậy O’ là giao điểm của A’C’ và B’D’.

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