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Giải bài 4.22 trang 89 SGK Toán 8 tập 1 - Kết nối tri thức

Cho tam giác ABC cân tại A có AB = 15 cm

🅺Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

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

Cho tam giác ABC cân tại A có AB = 15 cm, BC = 10 cm, đường phân giác trong của góc B cắt AC tại D. Khi đó, đoạn thẳng AD có độ dài là A. 3 cm. B. 6 cm. C. 9 cm. D. 12 cm.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

BD là đường phân giác của tam giác ABC, áp dụng tính chất của đường phân giác, tính độ dài đoạn thẳng AD.

Lời giải chi tiết

Đáp án đúng là: C

Vì tam giác ABC cân tại A nên AB = AC = 15 cm. Theo đề bài, BD là tia phân giác của \(\widehat {ABC}\), áp dụng tính chất đường phân giác vào tam giác ABC, ta có: \(\dfrac{{AB}}{{BC}} = \dfrac{{A{{D}}}}{{C{{D}}}} = \dfrac{{15}}{{10}} = \dfrac{3}{2}\) suy ra \(\dfrac{{A{{D}}}}{3} = \dfrac{{C{{D}}}}{2}\) Áp dụng tính chất dãy tỉ số bằng nhau, ta có: \(\dfrac{{A{{D}}}}{3} = \dfrac{{C{{D}}}}{2} = \dfrac{{A{{D}} + C{{D}}}}{{3 + 2}} = \dfrac{{AC}}{5} = \dfrac{{15}}{5} = 3\) Do đó AD = 3 . 3 = 9 (cm). Vậy AD = 9 cm.

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