Do GP là tia phân giác của \(\widehat{BGF}\)
\(\widehat{\Rightarrow FGP}=\widehat{PGB}=\frac{\widehat{BGF}}{2}\)
Do HP là tia phân giác \(\widehat{DHE}\)
\(\Rightarrow\widehat{DHP}=\widehat{EHP}=\frac{\widehat{DHE}}{2}\)
Trong tam giác GPH ta có
\(\widehat{FGP}+\widehat{EHP}+\widehat{GPH}=180^O\)
\(\Rightarrow\frac{\widehat{BGF}}{2}+\frac{\widehat{DHE}}{2}+\widehat{GPH}=180^O\)
\(\Rightarrow\frac{\widehat{BGF}+\widehat{DHE}}{2}+\widehat{GPH}=180^O\)
Do AB//CD
\(\Rightarrow\widehat{BGF}+\widehat{DHE}=180^O\) ( 2 góc trong cùng phía )
Ta có \(\frac{\widehat{BGF}+\widehat{DHE}}{2}+\widehat{GPH}=180^O\)
\(\Rightarrow\frac{180^O}{2}+\widehat{GPH}=180^0\)
\(\Rightarrow90^O+\widehat{GPH}=180^O\)
\(\Rightarrow\widehat{GPH}=180^O-90^O\)
\(\Rightarrow\widehat{GPH}=90^O\)
