if two lines intersect each other then prove that vertically opposite & angles
ese equel-
Answers
Step-by-step explanation:
As per the problem we need to prove, \angle \mathrm{AOD}=\angle \mathrm{BOC} \text { and } \angle \mathrm{AOC}=\angle \mathrm{BOD}∠AOD=∠BOC and ∠AOC=∠BOD
Now on line AB,
\angle \mathrm{AOD}+\angle \mathrm{BOD}=180^{\circ}∠AOD+∠BOD=180
∘
On line CD,
\angle \mathrm{BOC}+\angle \mathrm{BOD}=180^{\circ}∠BOC+∠BOD=180
∘
Hence, \angle \mathrm{AOD}+\angle \mathrm{BOD}=\angle \mathrm{BOC}+\angle \mathrm{BOD}∠AOD+∠BOD=∠BOC+∠BOD
\angle \mathrm{AOD}=\angle \mathrm{BOC}∠AOD=∠BOC --------------(Proved)
On line AB,
\angle \mathrm{AOC}+\angle \mathrm{BOC}=180^{\circ}∠AOC+∠BOC=180
∘
On Line CD,
\angle \mathrm{BOC}+\angle \mathrm{BOD}=180^{\circ}∠BOC+∠BOD=180
∘
Hence, \angle \mathrm{AOC}+\angle \mathrm{BOC}=\angle \mathrm{BOC}+\angle \mathrm{BOD}∠AOC+∠BOC=∠BOC+∠BOD
\angle \mathrm{AOC}=\angle \mathrm{BOD}∠AOC=∠BOD …………(Proved)
Hence the statement 'if two lines intersect each other then vertically opposite angles are equal' is proved