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Giải bài 4.19 trang 74 SGK Toán 7 tập 1 - Kết nối tri thức

Cho tia Oz là tia phân giác của góc xOy. Lấy các điểm A,B,C lần lượt thuộc các tia Ox, Oy, Oz sao cho

🔯Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Kết nối tri thức

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

Cho tia Oz là tia phân giác của góc xOy. Lấy các điểm A,B,C lần lượt thuộc các tia Ox, Oy, Oz sao cho \(\widehat {CAO} = \widehat {CBO}.\) a) Chứng minh rằng \(\Delta OAC = \Delta OBC\). b) Lấy điểm \(M\) trên tia đối của tia CO. Chứng minh rằng \(\Delta MAC = \Delta MBC\).

Phương pháp giải - Xem chi tiết

a)      Chứng minh hai tam giác bằng nhau theo trường hợp góc – cạnh – góc. b)      Chứng minh hai tam giác bằng nhau theo trường hợp cạnh – góc - cạnh.

Lời giải chi tiết

a) Trong \(\Delta OAC\) có: \(\widehat {AOC}+\widehat {OAC}+\widehat {OCA}=180^0\)Trong \(\Delta OBC\) có: \(\widehat {BOC}+\widehat {OBC}+\widehat {OCB}=180^0\)Mà \(\widehat {AOC} = \widehat {BOC}\)(do Oz là phân giác góc xOy) và \(\widehat {CAO}=\widehat {CBO}\) Do đó, \(\widehat {OCA}=\widehat {OCB}\).Xét \(\Delta OAC\) và \(\Delta OBC\) có:\(\widehat {AOC} = \widehat {BOC}\) (cmt)OC chung\(\widehat {OCA} = \widehat {OCB}(cmt)\)\(\Rightarrow \Delta OAC = \Delta OBC\)(g.c.g)b) Do \(\Delta OAC = \Delta OBC\) nên AC=BC ( 2 cạnh tương ứng)Vì \(\widehat {ACO}\) và \(\widehat {ACM}\) kề bù    \(\widehat {BCO}\) và \(\widehat {BCM}\) kề bùMà \(\widehat {ACO} = \widehat {BCO}\) nên \(\widehat {ACM} = \widehat {BCM}\)Xét \(\Delta MAC\) và \(\Delta MBC\) có:AC=BC (cmt)\(\widehat {ACM} = \widehat {BCM}\) (cmt)CM chung\( \Rightarrow \Delta MAC = \Delta MBC\)(c.g.c)

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