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Giải bài 6 trang 92 SGK Toán 7 tập 2 - Cánh diều

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ಞTổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Cánh diều

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

Cho \(\Delta ABC = \Delta MNP\). Tia phân giác của góc BAC và NMP lần lượt cắt các cạnh BC và NP tại D, Q. Chứng minh AD = MQ.

Phương pháp giải - Xem chi tiết

Chứng minh tam giác ABD bằng tam giác MNQ.

Lời giải chi tiết

Ta có: \(\Delta ABC = \Delta MNP\) nên theo tính chất 2 tam giác bằng nhau, ta có:\(\begin{array}{l}\widehat A = \widehat M,\widehat B = \widehat N,\widehat C = \widehat P\\AB = MN,BC = NP,AC = NP.\end{array}\)

Mà AD và MQ lần lượt là phân giác của góc BAC và NMP𒁃 nên \(\widehat {BAD} = \widehat {NMQ} = \dfrac{1}{2}\widehat {BAC} = \dfrac{1}{2}\widehat {NMP}\).

Xét hai tam giác ABD và MNQ có:

     \(\widehat {BAD} = \widehat {NMQ}\);

     AB = MN;

     \(\widehat B = \widehat N\).

Vậy \(\Delta ABD = \Delta MNQ\) (g.c.g) nên AD = MQ ( 2 cạnh tương ứng)

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