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Giải bài 3.29 trang 46 sách bài tập toán 7 - Kết nối tri thức với cuộc sống

Cho định lí: “ Tia đối của tia phân giác của một góc là tia phân giác của góc đối đỉnh của góc đó”. Hãy vẽ hình, ghi giả thiết, kết luận và chứng minh định lí đó.

♏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 định lí: “ Tia đối của tia phân giác của một góc là tia phân giác của góc đối đỉnh của góc đó”. Hãy vẽ hình, ghi giả thiết, kết luận và chứng minh định lí đó.

Phương pháp giải - Xem chi tiết

Chỉ ra các cặp góc đối đỉnh bằng nhau.

Lời giải chi tiết

GT: - \(\widehat {xOy};\widehat {x'Oy'}\) là 2 góc đối đỉnh       - Ou là tia phân giác của góc xOy, Ou’ là tia đối của tia Ou.KL: Ou’ là tia phân giác của \(\widehat {x'Oy'}\).

Chứng minh:

Ta có: \(\left\{ \begin{array}{l}\widehat {x'Ou'} = \widehat {xOu}\\\widehat {y'Ou'} = \widehat {yOu}\end{array} \right.\) (2 gốc đối đỉnh)Mà \(\widehat {xOu} = \widehat {yOu}\)(Ou là tia phân giác góc xOy)\( \Rightarrow \widehat {x'Ou'} = \widehat {y'Ou'}\)\( \Rightarrow \)Ou’ là tia phân giác của góc x’Oy’ (Ou’ nằm trong góc x’Oy’). 

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Tham Gia Group Dành Cho Lớp 7 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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