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Câu hỏi

Cho hình chóp có đáy là hình chữ nhật. . Gọi lần lượt là trung điểm của và . là điểm tùy ý trên cạnh ( không trùng với ) Xác định giao tuyến của các mặt phẳng và ; và . Xác định giao tuyến của các mặt phẳng và . Từ đó suy ra giao điểm N của và . Chứng minh rằng là hình thang cân.

Cho hình chóp  có đáy là hình chữ nhật.  .

Gọi  lần lượt là trung điểm của  và. là điểm tùy ý trên cạnh ( không trùng với )

  1. Xác định giao tuyến của các mặt phẳng  và ;.
  2. Xác định giao tuyến của các mặt phẳng  và . Từ đó suy ra giao điểm N của . Chứng minh rằng là hình thang cân.

T. ThuỳTrangNguyễn

Giáo viên

Xác nhận câu trả lời

Giải thích

Ta có Tương tự Do lần lượt là trung điểm của nên là đường trung bình của tam giác . Do đó (1) Ta có (2) Gọi là giao điểm của với . Ta có: . Từ (1) và (2) suy ra . Suy ra là hình thang. Dễ thấy ∆ S A D   = ∆ S B C c . c . c   →   S A D ^   =   S B C ^ " 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style="width: 276.00px; height: 17.33px; margin-left: 0.00px; margin-top: 0.00px; transform: rotate(0.00rad) translateZ(0px); -webkit-transform: rotate(0.00rad) translateZ(0px);" title="increment S A D space equals increment S B C open parentheses c. c. c close parentheses space rightwards arrow space stack S A D with hat on top space equals space stack S B C with hat on top"> → ∆ E A N   =   ∆ F B M   c . g . c   →   F M   =   E M " 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style="width: 296.00px; height: 12.00px; margin-left: 0.00px; margin-top: 0.00px; transform: rotate(0.00rad) translateZ(0px); -webkit-transform: rotate(0.00rad) translateZ(0px);" title="rightwards arrow increment E A N space equals space increment F B M space open parentheses c. g. c close parentheses space rightwards arrow space F M space equals space E M"> vậy là hình thang cân.

  1. Ta có

Tương tự

  1. Do lần lượt là trung điểm của  nên  là đường trung bình của tam giác . Do đó  (1)

Ta có  (2)

Gọi là giao điểm của với . Ta có:

.

Từ (1) và (2) suy ra