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Giải bài 3 (4.31) trang 76 vở thực hành Toán 7

Bài 3 (4.31). Cho năm điểm A, B,C,D,O như hình vẽ. Biết rằng OA = OB, OC = OD. a) Chứng minh rằng AC=BD. b) Chứng minh rằng \(\Delta ACD = \Delta BDC\)

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Đề bài

Bàiꦏ 3 (4.31). Cho năm điểm A, B,C,D,O như hình vẽ. Biết rằng OA = OB, OC = OD.

 

a) Chứng minh rằng AC=BD. b) Chứng minh rằng \(\Delta ACD = \Delta BDC\)

Phương pháp giải - Xem chi tiết

a) Chứng minh hai tam giác OAC và OBD bằng nhau b) Chứng minh hai tam giác ACD và BDC bằng nhau theo trường hợp c-c-c

Lời giải chi tiết

a) Xét hai tam giác OAC và OBD ta có:OA = OB (theo giả thiết)\(\widehat {AOC} = \widehat {BOD}\)(hai góc đối đỉnh)OC = OD (theo giả thiết)Vậy \(\Delta OAC = \Delta OBD\)( c – g –c). Do đó AC = BD.b) Xét hai tam giác ACD và BDC ta có:AC = BD (chứng minh trên)CD là cạnh chungAD = AO + OD = BO + OC = BCVậy \(\Delta ACD = \Delta BDC\)( c-c-c)

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