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Giải bài 54 trang 82 sách bài tập toán 8 – Cánh diều

Trong Hình 53, các điểm \(A,B,C,D\) lần lượt là các điểm nằm trên các đoạn thẳng \(IM,IN,IP,IQ\) sao cho

ꦏTổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Cánh diều

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

Trong Hình 53, các điểm \(A,B,C,D\) lần lượt là các điểm nằm trên các đoạn thẳng \(IM,IN,IP,IQ\) sao cho \(\frac{{IA}}{{IM}} = \frac{{IB}}{{IN}} = \frac{{IC}}{{IP}} = \frac{{ID}}{{IQ}} = \frac{1}{3}\). Quan sát Hình 53 và cho biết: a)      Hai hình bình hành \(MNPQ\) và \(A'B'C'D'\) có bằng nhau hay không; b)     Hai hình bình hành \(ABCD\) và \(A'B'C'D'\) có đồng dạng hay không.

 

Phương pháp giải - Xem chi tiết

Hình \(H'\) gọi là đồng dạng với hình \(H\) nếu hình \(H'\) bằng một hình nào đó đồng dạng phối cảnh với hình \(H\).

Lời giải chi tiết

a)      Quan sát Hình 53, ta thấy hai hình bình hành \(MNPQ\) và \(A'B'C'D'\) bằng nhau.b)     Hai hình bình hành \(ABCD\) và \(MNPQ\) đồng dạng phối cảnh và \(I\) là tâm đồng dạng phối cảnh. Mặt khác, hai hình bình hành \(MNPQ\) và \(A'B'C'D'\) bằng nhau. Do đó, hình bình hành \(ABCD\) đồng dạng với hình bình hành \(A'B'C'D'\).

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