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Giải bài 7 trang 75 vở thực hành Toán 7

Bài 7. Cho tam giác ABC và điểm D nằm trên cạnh BC sao cho AD vuông góc với BC và AD là phân giác góc BAC. Chứng minh rằng \(\Delta ABC\)cân tại A.

✱Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Kết nối tri thức

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

Bài♚ 7. Cho tam giác ABC và điểm D nằm trên cạnh BC sao cho AD vuông góc với BC và AD là phân giác góc BAC. Chứng minh rằng \(\Delta ABC\)cân tại A.

Phương pháp giải - Xem chi tiết

Tam giác cân là tam giác có hai cạnh bằng nhau.

Lời giải chi tiết

GT \(\Delta ABC\), \(D \in BC,AD \bot BC,\widehat {BAD} = \widehat {CAD}\)
KL  \(\Delta ABC\)cân tại A.
Hai tam giác ADB và ADC cùng vuông tại D và có:AD là cạnh chung\(\widehat {BAD} = \widehat {CAD}\)(theo giả thiết)Vậy \(\Delta ADB = \Delta ADC\)(cạnh góc vuông – góc nhọn).Do đó AB = AC hay \(\Delta ABC\)cân tại A.

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Tham Gia Group Dành Cho Lớp 7 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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