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Giải bài 4 trang 80 SGK Toán 8 tập 1– Chân trời sáng tạo

Cho hình bình hành

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

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

🐈Cho hình bình hành \(ABCD\) (\(AB > BC\)). Tia phân giác của góc \(D\) cắt \(AB\) tại \(E\), tia phân giác của góc \(B\) cắt \(CD\) tại \(F\)

a) Chứng minh \(DE\) // \(BF\)

b) Tứ giác \(DEBF\) là hình gì?

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

a) Chỉ ra cặp góc đồng vị bằng nhau b) Áp dụng dấu hiệu nhận biết hình bình hành

Lời giải chi tiết

a) Vì \(DE\), \(BF\) là phân giác (gt)

🅰Suy ra \(\widehat {{\rm{ADE}}} = \widehat {{\rm{EDC}}} = \frac{{\widehat {ADC}}}{2}\); \(\widehat {{\rm{EBF}}} = \widehat {{\rm{CBF}}} = \frac{{\widehat {ABC}}}{2}\) (1)

Vì \(ABCD\) là hình bình hành (gt)

🦄Suy ra \(AB\) // \(CD\) và \(\widehat {ADC} = \widehat {ABC}\) (2)

🅰Suy ra \(\widehat {{\rm{AED}}} = \widehat {{\rm{EDC}}}\) (so le trong) (3)

🥂Từ (1), (2), (3) suy ra \(\widehat {AED} = \widehat {ABF}\)

Mà hai góc ở vị trí đồng vị

Suy ra \(DE\) // \(BF\)

b) Xét tứ giác \(DEBF\) ta có:

\(DE\) // \(BF\) (cmt)

\(BE\) // \(DF\) (do \(AB\) // \(CD\))

Suy ra \(DEBF\) là hình bình hành

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