Có góc xOy và góc x'Oy' đối nhau
=> Góc xOy = Góc x'Oy'
Ta có: \(\left\{{}\begin{matrix}\widehat{xOm}=\widehat{mOy}=\widehat{xOy}:2\left(GT\right)\\\widehat{x'On}=\widehat{y'On}=\widehat{x'Oy'}:2\left(GT\right)\end{matrix}\right.\)
Mà: Góc xOy = Góc x'Oy' (cmt)
\(\Rightarrow\widehat{xOm}=\widehat{mOy}=\widehat{x'On}=\widehat{y'On}\)
Có: \(\left\{{}\begin{matrix}\widehat{xOy}+\widehat{x'Oy}=180^0\\\widehat{xOy'}+\widehat{x'Oy'}=180^0\end{matrix}\right.\) (kề bù)
Mà: Góc xOy = Góc x'Oy' (cmt)
=> Góc x'Oy = Góc xOy'
Ta có: \(\widehat{xOy}+\widehat{x'Oy}=180^0\left(kề-bù\right)\)
Hay: \(\widehat{xOm}+\widehat{mOy}+\widehat{x'Oy}=180^0\)
Mà: \(\left\{{}\begin{matrix}\widehat{yOm}=\widehat{y'On}\left(cmt\right)\\\widehat{xOy'}=\widehat{x'Oy}\left(cmt\right)\end{matrix}\right.\)
\(\Rightarrow\widehat{xOm}+\widehat{y'On}+\widehat{xOy'}=180^0\)
Hay: Gocs mOn = 1800
=> Om và On đối nhau
