Question

By paper cutting and pasting prove that If two lines intersect each other,

then the vertically opposite angles are equal. give diagram ​

Answer 1

Note

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