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Giải bài 1 (9.7) trang 69 vở thực hành Toán 7 tập 2

Cho hình vuông ABCD. Hỏi trong bốn đỉnh của hình vuông. a) Đỉnh nào cách đều hai điểm A và C? b) Đỉnh nào cách đều hai đường thẳng AB và AD?

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Đề bài

Cho hình vuông ABCD. Hỏi trong bốn đỉnh của hình vuông. a) Đỉnh nào cách đều hai điểm A và C? b) Đỉnh nào cách đều hai đường thẳng AB và AD?

Phương pháp giải - Xem chi tiết

a) Chứng minh \(AB = AD\) và \(CB = CD\) nên hai đỉnh B và D cách đều hai điểm A và C. b) + Chứng minh \(CB = CD\) nên C là một điểm cách đều hai đường thẳng AB và AD. + Chứng minh khoảng cách từ A đến hai đường AB, AD bằng nhau nên A là điểm cách đều hai đường thẳng AB và AD.

Lời giải chi tiết

a) Ta có \(AB = AD\) và \(CB = CD\) nên hai đỉnh B và D cách đều hai điểm A và C. b)
  • Ta có \(CB \bot AB\) nên CB là khoảng cách từ C đến AB. Tương tự, do \(CD \bot AD\) nên CD là khoảng cách từ C đến AD. Mặt khác ta có \(CB = CD\). Vậy C là một điểm cách đều hai đường thẳng AB và AD.
  • Vì điểm A nằm trên hai đường thẳng AB và AD nên khoảng cách từ A đến hai đường thẳng ấy bằng nhau. Vậy A cũng là một điểm cách đều hai đường thẳng AB và AD.

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