Mathematics

Two lines intersecting each other, prove that vertically opposite angles are equal.


SOLUTION
If two lines i.e. AB & CD intersect each other. They have two pair of opp. angles.

i.e.
$$\angle AOC , \angle DOB, \angle AOB, \angle COB.$$

To prove :- $$\angle AOC = \angle DOB $$ & $$\angle AOD = \angle COB$$

Proof :-
$$\angle AOC + \angle AOD = 180^{\circ}$$  [linear pair] ___(1)

$$\angle AOD + \angle BOD = 180^{\circ}$$   [linear pair] ___(2)

from eq. (1) & (2)

$$\angle AOC + \angle AOD = \angle AOD + \angle BOD$$

i.e.  $$[\angle AOC = \angle BOD]$$

Similarly $$[\angle AOD = \angle COB]$$ Hence proved.
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