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Giải bài tập 9.21 trang 83 SGK Toán 9 tập 2 - Kết nối tri thức

Cho hình thang ABCD (AB song song với CD) nội tiếp đường tròn (O). Chứng minh rằng ABCD là hình thang cân.

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

Toán - Văn - Anh
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Đề bài

Cho hình thang ABCD (AB song song với CD) nội tiếp đường tròn (O). Chứng minh rằng ABCD là hình thang cân.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

+ Chứng minh \(\widehat A + \widehat D = {180^o}\), \(\widehat A + \widehat C = {180^o}\) nên \(\widehat C = \widehat D\). + ABCD là hình thang và \(\widehat C = \widehat D\) nên ABCD là hình thang cân.

Lời giải chi tiết

Vì AB//CD nên \(\widehat A + \widehat D = {180^o}\) (hai góc trong cùng phía) Vì tứ giác ABCD là tứ giác nội tiếp nên \(\widehat A + \widehat C = {180^o}\) Do đó, \(\widehat C = \widehat D\). Hình thang ABCD có \(\widehat C = \widehat D\) nên ABCD là hình thang cân.

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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