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Bài 13 trang 170 Tài liệu dạy – học Toán 7 tập 1

Giải bài tập Chứng minh rằng tam giác ABC vuông trong các trường hợp sau :
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Đề bài

Chứng minh rằng tam giác ABC vuông trong các trường hợp sau : a) AB = 8 cm, AC = 15 cm, BC = 17 cm. b) AB = 29 cm, AC = 21 cm, BC = 20 cm. c) AB = 12 cm, AC = 37 cm, BC = 35 cm.

Lời giải chi tiết

\(a)A{B^2} = {8^2} = 64;A{C^2} = {15^2} = 225;B{C^2} = {17^2} = 289.\)Ta có: \(A{B^2} + A{C^2} = B{C^2}( = 289) \Rightarrow \Delta ABC\)  vuông tại A (theo định lý Pythagore đảo)\(b)A{B^2} = {29^2} = 841;A{C^2} = {21^2} = 441;B{C^2} = {20^2} = 400.\)Ta có: \(A{B^2} + A{C^2} = B{C^2}( = 841) \Rightarrow \Delta ABC\)  vuông tại C (theo định lý Pythagore đảo)\(c)A{B^2} = {12^2} = 144;A{C^2} = {37^2} = 1369;B{C^2} = {35^2} = 1225.\)Ta có: \(A{B^2} + A{C^2} = B{C^2}( = 1369) \Rightarrow \Delta ABC\)  vuông tại B (theo định lý Pythagore đảo)

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