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Giải bài 2 trang 71 SGK Toán 8 – Chân trời sáng tạo

Cho tứ giác

🍷Tổng 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 tứ giác \(ABCD\) có \(AB = AD\), \(BD\) là tia phân giác của góc \(B\). Chứng minh rằng \(ABCD\) là hình thang.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Chứng minh \(AD\) // \(BC\)

Lời giải chi tiết

𓃲Xét \(\Delta ABD\) ta có: \(AD = AB\) (gt) nên \( \Delta ADB\) cân tại \(A\)

Suy ra \( \widehat {ADB} = \widehat {ABD}\)

𓆉Mà \(\widehat {ABD} = \widehat {CBD}\) (do \(BD\) là phân giác của góc \(B\))

Do đó \(\widehat {ADB} = \widehat {CBD}\)

Mà hai góc ở vị trí so le trong

Suy ra \(AD\;{\rm{//}}\;BC\)

Suy ra \(ABCD\) là hình thang

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