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Giải bài tập 9.20 trang 83 SGK Toán 9 tập 2 - Kết nối tri thức

Cho hình bình hành ABCD nội tiếp đường tròn (O). Chứng minh rằng ABCD là hình chữ nhật.

Tổng hợp Đề thi vào 10 có đáp án và lời giải

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Đề bài

Cho hình bình hành ABCD nội tiếp đường tròn (O). Chứng minh rằng ABCD là hình chữ nhật.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Sử dụng tính chất hai góc đối nhau của hình bình hành bằng nhau và tứ giác nội tiếp có tổng hai góc đối nhau bằng \(180^0\) để chứng minh hình bình hành có một góc vuông là hình chữ nhật.

Lời giải chi tiết

Vì ABCD là hình bình hành nên \(\widehat A = \widehat C\). Mà hình bình hành ABCD nội tiếp đường tròn O nên \(\widehat A + \widehat C = 180^\circ\). Từ đó, ta có \(\widehat A = \widehat C = \frac{180^\circ}{2} = 90^\circ\). Hình bình hành ABCD có một góc vuông nên là hình chữ nhật.

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