Question

prove that vertically opposite angels are equal formed by two intersecting lines​

Answer 1

Step-by-step explanation:

Proof:

Note: Refer the image attached below

As per the problem we need to prove, \angle

$\mathrm{AOD}=\angle \mathrm{BOC} \text { and } \angle \mathrm{AOC}=\angle \mathrm{BOD}$

Now on line AB,

$\angle \mathrm{AOD}+\angle \mathrm{BOD}=180^{\circ}$

On line CD,

$\angle \mathrm{BOC}+\angle \mathrm{BOD}=180^{\circ}$

$</p><p>Hence, \: \angle \mathrm{AOD}+\angle \mathrm{BOD}=\angle \mathrm{BOC}+\angle \mathrm{BOD}$

$\angle \mathrm{AOD}=\angle \mathrm{BOC} --------------(Proved)</p><p>$

On line AB,

∠AOC+∠BOC=180°

On Line CD,

∠BOC+∠BOD=180°

∠AOC+∠BOC=∠BOC+∠BOD

∠AOC=∠BOD …………(Proved)

Hence the statement 'if two lines intersect each other then vertically opposite angles are equal' is proved.

Answer 2

Answer:

Proof:

Note: Refer the image attached below

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

∘

< /p > < p > Hence, \: \angle \mathrm{AOD}+\angle \mathrm{BOD}=\angle \mathrm{BOC}+\angle \mathrm{BOD}</p><p>Hence,∠AOD+∠BOD=∠BOC+∠BOD

\angle \mathrm{AOD}=\angle \mathrm{BOC} --------------(Proved) < /p > < p >∠AOD=∠BOC−−−−−−−−−−−−−−(Proved)</p><p>

On line AB,

∠AOC+∠BOC=180°

On Line CD,

∠BOC+∠BOD=180°

∠AOC+∠BOC=∠BOC+∠BOD

∠AOC=∠BOD …………(Proved)

Hence the statement 'if two lines intersect each other then vertically opposite angles are equal' is proved.