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Giải bài 1.13 trang 20 Chuyên đề học tập Toán 11 Kết nối tri thức

Cho hình bình hành ABCD với tâm O.

⛦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 bình hành ABCD với tâm O. a) Tìm ảnh của đường thẳng AB qua phép đối xứng tâm O. b) Tìm ảnh của tam giác ABC qua phép đối xứng tâm O.

Phương pháp giải - Xem chi tiết

- Tìm ảnh của từng điểm A, B, C qua phép đối xứng tâm O. Sau đó nối chúng với nhau ta được ảnh của AB, tam giác ABC qua phép đối xứng tâm O. - Cho điểm O, phép biến hình biến điểm O thành chính nó và biến mỗi điểm \(M \ne O\) thành điểm M’ sao cho O  là trung điểm của MM’ được gọi là phép đối xứng tâm O . Điểm O được gọi là tâm đối xứng.

Lời giải chi tiết

Vì ABCD là hình bình hành nên tâm O là trung điểm các đường chéo AC và BD.Vì O là trung điểm của AC nên C là ảnh của A qua phép đối xứng tâm O.Vì O là trung điểm của BD nên D là ảnh của B qua phép đối xứng tâm O.Do đó, CD là ảnh của đường thẳng AB qua phép đối xứng tâm O.Lại có A là ảnh của C qua phép đối xứng tâm O. Vậy tam giác CDA là ảnh của tam giác ABC qua phép đối xứng tâm O.

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