Question

prove vertically opposite angle theorem​

Answer 1

${\huge{\boxed{\underline{\pink{Ans}\purple{wer}}}}}$

Given :-

Two lines AB and CD intersecting at point O.

To prove :-

Vertically opposite angles are equal

i.e, angle AOC = angle BOD

angle AOD = angle BOC

Proof :-

On line AB,

By linear pair,

angle AOD + angle AOC = 180° (equation 1)

On line CD

By linear pair ,

angle AOD + angle AOC = 180° (equation 2)

From equation (1) and (2) :-

AOC + BOC = AOD + AOC

→ BOC = AOD

Now :-

To prove , angle AOC = angle BOD :-

On line AB,

By linear pair ,

AOD + BOD = 180° (equation 3)

On line CD,

By linear pair,

AOD + AOC = 180° (equation 4)

From equation (3) and (4) :-

AOD + BOD = AOD + AOC

→ BOD = AOC

Hence , Vertically Opposite angles are equal :-

Answer 2

${\huge{\boxed{\underline{\pink{Ans}\purple{wer}}}}}$

Given :-

Two lines AB and CD intersecting at point O.

To prove :-

Vertically opposite angles are equal

i.e, angle AOC = angle BOD

angle AOD = angle BOC

Proof :-

On line AB,

By linear pair,

angle AOD + angle AOC = 180° (equation 1)

On line CD

By linear pair ,

angle AOD + angle AOC = 180° (equation 2)

From equation (1) and (2) :-

AOC + BOC = AOD + AOC

→ BOC = AOD

Now :-

To prove , angle AOC = angle BOD :-

On line AB,

By linear pair ,

AOD + BOD = 180° (equation 3)

On line CD,

By linear pair,

AOD + AOC = 180° (equation 4)

From equation (3) and (4) :-

AOD + BOD = AOD + AOC

→ BOD = AOC

Hence , Vertically Opposite angles are equal :-