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Giải bài 4.6 trang 67 SGK Toán 7 tập 1 - Kết nối tri thức

Cho Hình 4.20, biết AB = CB,AD = CD,

🌞Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Kết nối tri thức

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

Cho Hình 4.20, biết \(AB = CB, AD = CD,\widehat{DAB} = {90^\circ },\widehat{BDC} = {30^\circ }\)

a) Chứng minh rằng \(\Delta ABD = \Delta CBD\). b) Tính \(\widehat {ABC}\).

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

a) Chứng minh hai tam giác bằng nhau bằng cách chỉ ra 3 cặp cạnh bằng nhau (c.c.c). b) \(\widehat {ABC} = \widehat {ABD} + \widehat {CBD}\)

Lời giải chi tiết

a)      Xét \(\Delta ABD\) và \(\Delta CBD\)có: DA=DC(gt) BD chung BA=BC Vậy \(\Delta ABD = \Delta CBD\)(c.c.c) b)     Ta có \(\widehat A = \widehat C = {90^o}\)(hai góc tương ứng) Theo định lí tổng ba góc trong tam giác BCD, ta có: \(\widehat C + \widehat {CDB} + \widehat {DBC} = {180^o}\) \({90^o} + {30^o} + \widehat {DBC} = {180^o}\) Suy ra \(\widehat {DBC} = {60^o}\) Mà \(\Delta ABD = \Delta CBD\) nên \(\widehat {ABD} = \widehat {CBD}\) (2 góc tương ứng) Suy ra \(\widehat {ABD} = \widehat {CBD} = {60^o}\) Do đó \(\widehat {ABC} = \widehat {ABD} + \widehat {CBD} = {60^o} + {60^o} = {120^o}\)

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Tham Gia Group Dành Cho Lớp 7 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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