cho tam giác abc. vẽ BD vuông góc với AC. CE vuông góc với AB. Gọi M là trung điểm của BC. N là trung điểm của DE. Chứng minh rằng MN vuông góc với DE
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Cho tam giác ABC kẻ BD vuông góc với AC,CE vuông góc với AB. Gọi M, N lần lượt là trung điểm BC và DE. Chứng minh MN vuông góc với DE.
ai làm ơn làm phước tick cho mk vài cái cho lên 160 điểm hỏi đáp với
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mình van xin các bạn hãy cho mình 4 cái tick thôi chỉ 4 cái thôi
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Cho tam giác ABC có AC > AB. Gọi N là trung điểm của BC. Kẻ BD vuông góc với AM tại D, CE vuông góc với AM tại E.
Chứng minh rằng:
a; BD = CE
b; M là trung điểm của DE
1. Cho tam giác ABC , hai đường cao BD, CE. Gọi M, N lần lượt là trung điểm của BC, DE. Chứng minh MN vuông góc với DE?2. Cho tam giác ABC có góc A 900. Trên nữa mặt phẳng bờ AB có chứa điểm C vẽ AD vuông góc với AB và ADAB, trên nữa mặt phẳng bờ AC có chứa điểm B vẽ AE vuông góc với AC và AEAC. Kẻ AH vông góc với ED (H thuộc ED). Chứng minh rằng đường thẳng Ah đi qua trung điểm M của cạnh BC.
Đọc tiếp
1. Cho tam giác ABC , hai đường cao BD, CE. Gọi M, N lần lượt là trung điểm của BC, DE. Chứng minh MN vuông góc với DE?
2. Cho tam giác ABC có góc A <900. Trên nữa mặt phẳng bờ AB có chứa điểm C vẽ AD vuông góc với AB và AD=AB, trên nữa mặt phẳng bờ AC có chứa điểm B vẽ AE vuông góc với AC và AE=AC. Kẻ AH vông góc với ED (H thuộc ED). Chứng minh rằng đường thẳng Ah đi qua trung điểm M của cạnh BC.
Cho tam giác ABC. Vẽ đường cao BD, CE. M,N là trung điểm của BC, DE. Chứng minh rằng MN vuông góc với DE
Cho tam giác ABC. Vẽ đường cao BD, CE. M,N là trung điểm của BC, DE. Chứng minh rằng MN vuông góc với DE
1. Cho tam giác ABC vuông ở A có AB<AC. AH vuông góc với BC tại H, D là điểm trên cạnh BC sao cho AD=AB. Vẽ DE vuông góc với BC tại E. Chứng mih rằng AH=HE.
2. Cho tam giác ABC vuông cân tại A.. Qua A vẽ đường thẳng d ở ngoài tam giác ABC . Vẽ BD vuông góc với d taị D. CE vuông góc với d tại E. M là trung điểm CB. Chứng minh rằng:
a) BD + CE = DE
b) Tam giác MDE là tam giác vuông cân
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Xem thêm câu trả lời
Cho tam giác ABC. Vẽ tia BD sao cho BD vuông góc với AC ; vẽ tia EC vuông góc với AB. M , N lần lượt là trung điểm của BC; DE .CMR: MN vuông góc với DE
Nối EM; DM. Chứng minh được EM = DM vì cùng = BC/2
+) Bài toán phụ : Nếu tam giác ABC có trung tuyến AM thì AM = BC/2
Chứng minh:
Trên tia đối của tia MA lấy D sao cho MA = MD
- Tam giác AMB = DMC ( c - g- c) vì: AM = DM; góc AMB = DMC (đối đỉnh); MB = MC
=> góc ABM = MCD ( 2 góc tương ứng) Mà 2 góc này ở vị trí so le trong nên AB // CD
Ta có: AB | AC nên CD | AC =>góc ACD = 90o
- Tam giác ABC = tam giác CDA (c- g- c) vì: chung cạnh AC; góc BAC = DCA (= 90o) ; AB = CD
=> BC = DA Mà AM = DA/2 nên AM = BC/2 (đpcm)
+) Áp dụng:
Tam giác BEC vuông tại E (do CE | AB ) có EM là trung tuyến nên EM = BC/2
Tam giác BDC vuông tại D (do BD | AC) có DM là trung tuyến nên DM = BC/2
=> EM = DM => tam giác AMD cân tại M
Lại có MN là trung tuyến (do N là trung điểm của DE) nên đồng thời là đường cao
=> MN | DE (đpcm)
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Cho tam giác ABC. Vẽ tia BD sao cho BD vuông góc với AC ; vẽ tia EC vuông góc với AB. M , N lần lượt là trung điểm của BC; DE .CMR: MN vuông góc với DE
Cho tam giác ABC; 2 đường cao BD, CE. Gọi M,N lần lượt là trung điểm của BC, DE. Chứng minh MN vuông góc với DE