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Giải bài 4 trang 92 SGK Toán 7 tập 2 - Cánh diều

Cho Hình 67 có

🐻Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Cánh diều

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

Cho Hình 67 có \(\widehat {AHD} = \widehat {BKC} = 90^\circ ,DH = CK,\widehat {DAB} = \widehat {CBA}\). Chứng minh AD = BC.

Phương pháp giải - Xem chi tiết

Chứng minh tam giác AHD bằng tam giác BKC.

Lời giải chi tiết

Ta có: \(\widehat {DAB} = \widehat {CBA}\)Mà \(\widehat {DAB} +\widehat {HAD} =180^0; \widehat {CBA}= \widehat {KBC}\) (2 góc kề bù)\(\Rightarrow \widehat {HAD} = \widehat {KBC}\) Mà tổng ba góc trong tam giác bằng 180° và \(\widehat {AHD} = \widehat {BKC} = 90^\circ ,\widehat {HAD} = \widehat {KBC}\) nên \(\widehat {ADH} = \widehat {BCK}\).

Xét tam giác AHD và tam giác BKC có:

     \(\widehat {AHD} = \widehat {BKC}\);

     HD = KC;

     \(\widehat {ADH} = \widehat {BCK}\).

Vậy \(\Delta AHD = \Delta BKC\)(g.c.g) nên AD = BC ( 2 cạnh tương ứng)

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