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Giải bài 4.32 trang 86 SGK Toán 7 tập 1 - Kết nối tri thức

Cho tam giác MBC vuông tại M có B= 60°. Gọi A là điểm nằm trên tia đối của tia MB sao cho MA = MB. Chứng minh rằng tam giác ABC là tam giác đều.

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Đề bài

Cho tam giác MBC vuông tại M có \(\widehat B\) = 60°. Gọi A là điểm nằm trên tia đối của tia MB sao cho MA = MB. Chứng minh rằng tam giác ABC là tam giác đều.

Phương pháp giải - Xem chi tiết

Chứng minh tam giác ABC cân tại C và có 1 góc bằng 60 độ.

Lời giải chi tiết

Xét \(\Delta CMB\) và \(\Delta CMA\) có:MC chung\(\widehat{BMC}=\widehat{AMC}(=90^0)\)MB=MA (gt)=> \(\Delta CMB = \Delta CMA\)(c.g.c)=> CA = CB (2 cạnh tương ứng).=> Tam giác ABC cân tại C.

 Mà \(\widehat B=\) 60o

=> Tam giác ABC đều.

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