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Giải bài 4 trang 40 Chuyên đề học tập Toán 11 Chân trời sáng tạo

Tìm các hình đồng dạng với nhau trong Hình 6.

Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Chân trời sá𝓰ng tạo

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

Tìm các hình đồng dạng với nhau trong Hình 6.

Phương pháp giải - Xem chi tiết

Quan sát hình 6 và tìm những hình có hình dạng giống nhau (kích thước có thể khác nhau).

Lời giải chi tiết

⦁ Ta xét hình hai ngôi nhà:

 

Giả sử O là điểm cố định và A là một điểm trên hình ngôi nhà 1 (hình vẽ).Lấy điểm A’ trên hình ngôi nhà 2 có vị trí tương ứng với điểm A trên hình ngôi nhà 1.Khi đó ta có ba điểm O, A, A’ thẳng hàng và A, A’ nằm cùng phía đối với O.Suy ra \(\overrightarrow {OA'}  = k\overrightarrow {OA} \), với k > 0.Do đó \({V_{\left( {O,{\rm{ }}k} \right)}}\left( A \right){\rm{ }} = {\rm{ }}A',{\rm{ }}OA'{\rm{ }} = {\rm{ }}k.OA.\)Vì vậy \(k = \frac{{OA'}}{{OA}}\)Chọn một điểm B trên hình ngôi nhà 1 sao cho \(B{\rm{ }} \ne {\rm{ }}A.\)Lấy điểm B’ sao cho \(\overrightarrow {OB'}  = k\overrightarrow {OB} \)Khi đó \({V_{\left( {O,\frac{{OA'}}{{OA}}} \right)}}\left( B \right) = B'\) và điểm B’ là một điểm trên hình ngôi nhà 2 có vị trí tương ứng với điểm B trên hình ngôi nhà 1.Tương tự như vậy, với mỗi điểm M bất kì trên hình ngôi nhà 1, ta lấy điểm M’ sao cho \({V_{\left( {O,\frac{{OA'}}{{OA}}} \right)}}\left( M \right) = M'\)  thì ta được tập hợp các điểm M’ tạo thành hình ngôi nhà 2.
Vì vậy \({V_{\left( {O,\frac{{OA'}}{{OA}}} \right)}}\) biến hình ngôi nhà 1 thành hình ngôi nhà 2.Vì vậy phép đồng dạng tỉ số \(\frac{{OA'}}{{OA}}\) biến hình ngôi nhà 1 thành hình ngôi nhà 2.Do đó hình ngôi nhà 1 và hình ngôi nhà 2 đồng dạng với nhau.Chứng minh tương tự cho hình hai chiếc smartphone, ta cũng được kết quả như trên.Vậy ta có hình hai ngôi nhà và hình hai chiếc smartphone đồng dạng với nhau trong Hình 6.

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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