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Giải bài 4.59 trang 74 sách bài tập toán 7 - Kết nối tri thức với cuộc sống

Cho Hình 4.61, hãy tính số đo các góc của tam giác ABE.

﷽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 4.61, hãy tính số đo các góc của tam giác ABE.

Phương pháp giải - Xem chi tiết

-Tính các góc của tam giác ACD -Tính các góc ABC, BAC (Tam giác ABC cân tại C) -Tính các góc AED, DAE (Tam giác ADE cân tại D).

Lời giải chi tiết

Tam giác ACD đều, nên \(\widehat {ACD} = \widehat {ADC} = \widehat {CAD} = {60^0}\)Tam giác ABC cân tại đỉnh C nên:\(\widehat {ABC} = \widehat {BAC} = \dfrac{{\widehat {ABC} + \widehat {BAC}}}{2} = \dfrac{{{{180}^0} - \widehat {ACB}}}{2} = \dfrac{{\widehat {ACD}}}{2} = {30^0}.\)Tam giác ADE cân tại đỉnh D nên:\(\widehat {AED} = \widehat {DAE} = \dfrac{{\widehat {AED} + \widehat {DAE}}}{2} = \dfrac{{{{180}^0} - \widehat {ADE}}}{2} = \dfrac{{\widehat {ADC}}}{2} = {30^0}\)Do vậy, ta có:\(\widehat {ABE} = \widehat {ABC} = {30^0};\widehat {AEB} = \widehat {AED} = {30^0};\widehat {BAE} = {180^0} - \widehat {ABE} - \widehat {AEB} = {120^0}\). 

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

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