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Giải bài 9.8 trang 90 SGK Toán 8 tập 2 - Kết nối tri thức

Cho tam giác ABC có AB=12cm

🍃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 có AB=12cm, AC=15cm. Trên các tia AB, AC lần lượt lấy các điểm M, N sao cho AM=10cm, AN=8cm. Chứng minh rằng ΔABC ∽ ΔANM.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

🎃- Chứng minh: \(\frac{{AN}}{{AB}} = \frac{{AM}}{{AC}}\)

𝓀- Chứng minh hai tam giác ABC và tam giác ANM có hai cạnh tương ứng tỉ lệ và góc A chung nên hai tam giác ABC và tam giác ANM đồng dạng với nhau.

Lời giải chi tiết

Có  AB=12cm , AN=8cm => \(\frac{{AN}}{{AB}} = \frac{8}{{12}} = \frac{2}{3}\) AC=15cm,  AM=10cm => \(\frac{{AM}}{{AC}} = \frac{{10}}{{15}} = \frac{2}{3}\) => \(\frac{{AN}}{{AB}} = \frac{{AM}}{{AC}}\) - Xét hai tam giác ABC và tam giác ANM, có \(\frac{{AN}}{{AB}} = \frac{{AM}}{{AC}}\), góc A chung

=> ΔABC ∽ ΔANM (c.g.c) 

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