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Giải bài 3 trang 92 SGK Toán 7 tập 2 - Cánh diều

Cho Hình 66 có

✃Tổng 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 Hình 66 có \(\widehat N = \widehat P = 90^\circ ,\widehat {PMQ} = \widehat {NQM}\). Chứng minh MN = QP, MP = QN.

Phương pháp giải - Xem chi tiết

Chứng minh hai tam giác MNQ bằng tam giác QPM.

Lời giải chi tiết

Ta có: tổng ba góc trong một tam giác bằng 180° và \(\widehat N = \widehat P = 90^\circ ,\widehat {PMQ} = \widehat {NQM}\) nên \(\widehat {PQM} = \widehat {NMQ}\).

Xét hai tam giác MNQ và QPM có:

\(\widehat {NQM}=\widehat {PMQ}\)

MQ chung

\(\widehat {NMQ}=\widehat {PQM}\)

Vậy \(\Delta MNQ = \Delta QPM\)(g.c.g). Do đó MN = QP, MP = QN ( 2 cạnh tương ứng)

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