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Giải bài 6 trang 72 SGK Toán 8 – Chân trời sáng tạo

Cho hình thang cân

൲Tổng 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

𓆉Cho hình thang cân \(ABCD\) có \(AB\) // \(CD\). Qua giao điểm \(E\) của \(AC\) và \(BD\), ta vẽ đường thẳng song song với \(AB\) và cắt \(AD\), \(BC\) lần lượt tại \(F\) và \(G\) (Hình 16). Chứng minh rằng \(EG\) là tia phân giác của góc \(CEB\).

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

ﷺChứng minh \(\widehat {{\rm{CEG}}} = \widehat {{\rm{BEG}}}\)

Lời giải chi tiết

Vì \(EG\) // \(AB\) (gt)

𝓀suy ra \(\widehat {{\rm{CEG}}} = \widehat {{\rm{CAB}}}\) (đồng vị) và \(\widehat {{\rm{GEB}}} = \widehat {{\rm{EBA}}}\) (so le trong) (1)

Xét \(\Delta CAB\) và \(\Delta DBA\) ta có:

\(AC = BD\) (tính chất hình thang cân)

\(BC = AD\) (tính chất hình thang cân)

\(AB\) chung

Suy ra \(\Delta CAB = \Delta DBA\) (c-c-c)

ꦬSuy ra \(\widehat {{\rm{CAB}}} = \widehat {{\rm{EBA}}}\) (hai góc tương ứng) (2)

⛎Từ (1) và (2) suy ra \(\widehat {{\rm{CEG}}} = \widehat {{\rm{GEB}}}\)

🎐Suy ra \(EG\) là phân giác của \(\widehat {{\rm{CEB}}}\)

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Tham Gia Group Dành Cho Lớp 8 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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