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Giải bài 2 trang 60 sách bài tập toán 8 - Chân trời sáng tạo

Tứ giác ABCD có \(\widehat A + \widehat D = \widehat B + \widehat C\). Chứng minh tứ giác ABCD là hình thang.

🌜Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Chân trời sáng tạo

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Đề bài

Tứ giác ABCD có \(\widehat A + \widehat D = \widehat B + \widehat C\). Chứng minh tứ giác ABCD là hình thang.

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức về dấu hiệu nhận biết hình thang để chứng minh: Tứ giác có hai cạnh đối song song là hình thang.

Lời giải chi tiết

Tứ giác ABCD có: \(\widehat A + \widehat B + \widehat C + \widehat D = {360^0}\)Mà \(\widehat A + \widehat D = \widehat B + \widehat C\) nên \(2\left( {\widehat A + \widehat D} \right) = {360^0}\)\(\widehat A + \widehat D = {180^0}\), suy ra AB//CDTứ giác ABCD có: AB//CD nên tứ giác ABCD là hình thang.

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