Question

[Nguyễn Hữu Vĩnh Thịnh]

Trong hình trên, biết:  \(\widehat{NMO}=\alpha^o;\widehat{OPQ}=\beta^o;\widehat{MOP}=\alpha^o+\beta^o\) \(\left(0^o< \alpha^o;\beta^o< 90^o\right)\)

Hãy chứng tỏ: MN//PQ

Answer 1

[๓เภђ ภوยץễภ ђảเ]

Kẻ \(Oz//MN\)

\(\Rightarrow\widehat{NMO}+\widehat{MOz}=180^o\)

\(\Rightarrow\alpha+\widehat{MOz}=180^o\)

\(\Rightarrow\widehat{MOz}=180^o-\alpha\)

Ta có

\(\widehat{MOz}+\widehat{MOP}+\widehat{zOP}=360^o\)

\(\Rightarrow\widehat{zOP}+180^o-\alpha+\alpha+\beta=360^o\)

\(\Rightarrow\widehat{zOP}+180^o-\alpha+\alpha+\beta=360^o\)

\(\Rightarrow\widehat{zOP}=360^o-\alpha+\alpha-\beta-180^o\)

\(\Rightarrow\widehat{zOP}=180^o-\beta\)

Suy ra 

\(\Rightarrow\widehat{zOP}+\widehat{OPQ}=180^o-\beta+\beta=180^o\) mà chúng là 2 góc trong cùng phía

\(\Rightarrow MN//PQ\)