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Giải bài 4 (4.32) trang 77 vở thực hành Toán 7

Bài 4 (4.32). Cho tam giác MBC vuông tại M có \(\widehat B = {60^o}\). 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.

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

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Đề bài

Bài💟 4 (4.32). Cho tam giác MBC vuông tại M có \(\widehat B = {60^o}\). 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

Tam giác đều là tam giác có ba cạnh bằng nhau và ba góc bằng nhau.

Lời giải chi tiết

GT \(\Delta MBC,\widehat M = {90^o},\widehat B = {60^o},MA = MB\) A thuộc tia đối của tia MB
KL \(\Delta ABC\)đều.
Ta thấy hai tam giác MBC và MAC vuông tại M và có:MB = MA (theo giả thiết)MC là cạnh chungVậy \(\Delta MBC = \Delta MAC\)(hai cạnh góc vuông). Do đó \(\widehat A = \widehat B = {60^o}\)Suy ra \(\widehat C = {180^o} - \widehat A - \widehat B = {60^o}\)Vậy ABC là tam giác có ba góc bằng nhau nên đây là tam giác đều.

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