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Giải bài 6 (4.28) trang 75 vở thực hành Toán 7

Bài 6 (4.28). Cho tam giác ABC cân tại A có đường cao AD. Chứng minh rằng đường thẳng AD là đường trung trực của đoạn thẳng BC.

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Đề bài

Bài🥃 6 (4.28). Cho tam giác ABC cân tại A có đường cao AD. Chứng minh rằng đường thẳng AD là đường trung trực của đoạn thẳng BC.

Phương pháp giải - Xem chi tiết

Đường trung trực của đoạn thẳng  là đường thẳng vuông góc và đi qua trung điểm của đoạn thẳng.

Lời giải chi tiết

GT \(\Delta ABC\)cân tại A, \(AD \bot BC = D\)
KL  AD là trung trực BC.
Ta thấy tam giác ADB và tam giác ADC vuông tại D và có:AB = AC (\(\Delta ABC\)cân tại A)AD là cạnh chungVậy \(\Delta ADB = \Delta ADC\)(cạnh huyền – cạnh góc vuông). Do đó DB = DC.Vậy D là trung điểm của BC và AD là trung trực của đoạn thẳng BC.

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