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Giải bài 3 trang 60 sách bài tập toán 8 - Chân trời sáng tạo

Cho tam giác ABC vuông cân tại A. Vẽ ra phía ngoài của tam giác ABC một tam giác BCD vuông cân tại B. Tứ giác ABDC là hình gì? Vì sao?

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

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Đề bài

Cho tam giác ABC vuông cân tại A. Vẽ ra phía ngoài của tam giác ABC một tam giác BCD vuông cân tại B. Tứ giác ABDC là hình gì? Vì sao?

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức về hình thang vuông để chứng minh: Hình thang có một góc vuông được gọi là hình thang vuông.

Lời giải chi tiết

Tam giác ABC vuông cân tại A nên \(\widehat {{B_1}} = {45^0},\widehat A = {90^0}\)Tam giác BCD vuông cân tại B nên \(\widehat {{C_1}} = {45^0}\)Do đó, \(\widehat {{B_1}} = \widehat {{C_1}}\), mà hai góc này ở vị trí so le trong nên AB//CDDo đó, tứ giác ABDC là hình thang.Mà \(\widehat A = {90^0}\) nên tứ giác ABDC là hình thang vuông.

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