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Giải bài 1 trang 81 SGK Toán 8 – Cánh diều

Cho Hình 74. a) Chứng minh

🌟Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Cánh diều

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

Cho Hình 74.

a) Chứng minh \(\Delta ABC \backsim \Delta MNP\) b) Góc nào của tam giác MNP bằng góc B? c) Góc nào của tam giác ABC bằng góc P?

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

a) Sử dụng trường hợp đồng dạng thứ hai để chứng minh hai tam giác đồng dạng. b) Sử dụng định nghĩa hai tam giác đồng dạng để tìm ta các góc bằng nhau. c) Sử dụng định nghĩa hai tam giác đồng dạng để tìm ta các góc bằng nhau.

Lời giải chi tiết

a) Ta thấy \(\frac{{AB}}{{MN}} = \frac{4}{3};\,\,\frac{{AC}}{{MP}} = \frac{5}{{3,75}} = \frac{4}{3}\) \( \Rightarrow \frac{{AB}}{{MN}} = \frac{{AC}}{{MP}}\) Xét tam giác ABC và tam giác MNP có: \(\frac{{AB}}{{MN}} = \frac{{AC}}{{MP}}\) và \(\widehat {BAC} = \widehat {NMP} = 60^\circ \) \( \Rightarrow \Delta ABC \backsim \Delta MNP\) (c-g-c) b) Vì \(\Delta ABC \backsim \Delta MNP\) (chứng minh ở câu a) nên \(\widehat N = \widehat B\). c) Vì \(\Delta ABC \backsim \Delta MNP\) (chứng minh ở câu a) nên \(\widehat C = \widehat P\).

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