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Giải bài 9.9 trang 52 sách bài tập toán 8 - Kết nối tri thức với cuộc sống

Cho hình bình hành ABCD có E, F lần lượt là trung điểm của AB và AC. Chứng minh $\Delta AEF\backsim \Delta CDA$

💜Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

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

Cho hình bình hành ABCD có E, F lần lượt là trung điểm của AB và AC. Chứng minh $\Delta AEF\backsim \Delta CDA$ 

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức định lí (một trường hợp đặc biệt của hai tam giác đồng dạng) để chứng minh hai tam giác đồng dạng: Nếu một đường thẳng cắt hai cạnh của một tam giác và song song với cạnh còn lại thì nó tạo thành một tam giác mới đồng dạng với tam giác đã cho.

Lời giải chi tiết

Vì ABCD là hình bình hành nên \(\widehat B = \widehat D,AB = CD,BC = AD\)Do đó, \(\Delta ABC = \Delta CDA\left( {c.g.c} \right)\) (1)Tam giác ABC có E, F lần lượt là trung điểm của AB và AC nên EF là đường trung bình tam giác ABC. Do đó, EF//BCTam giác ABC có: EF//BC nên $\Delta AEF\backsim \Delta ABC$ (2)Từ (1) và (2) suy ra: $\Delta AEF\backsim \Delta CDA$

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