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Giải bài 2 trang 111 SGK Toán 8 tập 1 - Cánh diều

Cho tam giác ABC vuông tại

▨Tổng 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

Cho tam giác ABC vuông tại A có M là trung điểm của cạnh BC. Trên tia đối của tia MA lấy điểm D sao cho MD = MA. Chứng minh tứ giác ABCD là hình chữ nhật và \(AM = \dfrac{1}{2}BC\).

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

🥂Chứng minh ABCD là hình bình hành có hai đường chéo bằng nhau.

Lời giải chi tiết

Xét tứ giác ABCD có:MB = MC (M là trung điểm của BC)MA = MD (gt)Suy ra tứ giác ABDC là hình bình hành (có hai đường chéo cắt nhau tại trung điểm của mỗi đường)Mà hình bình hành ABDC có \(\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over A}  = {90^0}\)nên ABCD là hình chữ nhậtVì: ABDC là hình chữ nhật nên BC = ADMà: \(AM = \dfrac{1}{2}AC = \dfrac{1}{2}BC\)

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