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Bài tập 15 trang 153 Tài liệu dạy – học Toán 7 tập 1

Giải bài tập Cho hình 44 có AB = AC, BD = CD. Chứng minh rằng:
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Đề bài

Cho hình 44 có AB = AC, BD = CD. Chứng minh rằng: a) \(\Delta ABD = \Delta ACD\) b) AD là tia phân giác của góc BAC.

 

Lời giải chi tiết

a)Xét tam giác ABD và ACD có:AB = AC (gt)BD = CD (gt)AD là cạnh chungDo đó: \(\Delta ABD = \Delta ACD(c.c.c)\)b) Ta có: \(\Delta ABD = \Delta ACD\)  (chứng minh câu a) \( \Rightarrow \widehat {BAD} = \widehat {CAD}\)Mà AD nằm giữa AB, ACDo đó: AD là tia phân giác của góc BAC.

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