Question

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

Answer 1

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.