Question

Prove that, if two lines intersect each other, then the vertically opposite angles are equal.

Answer 1

↬ Given :-

• Two line AB and CD intersect at a point O.

↬ To prove :-

• ∠ AOD = ∠ BOC
• ∠AOC = ∠ BOD

↬ Proof :-

$\rm\angle{AOD}+\angle{AOC}=180\degree\:\:\:\:(linear\:pair)\:............(i)$

$\rm\angle{AOC}+\angle{BOC}=180\degree\:\:\:\:(linear\:pair)\:...........(ii)$

⤤ From eq (i) and (ii) we get,

$\rm\angle{AOD}+\cancel{\angle{AOC}}=\cancel{\angle{AOC}}+\angle{BOC}$

$\rm\angle{AOD}=\angle{BOC}$

Similarly,

$\rm\angle{AOC}=\angle{BOD}$

$\rm\:Hence,Proved$

${\underline{\boxed{\bf\red{More\:Information}}}}$

⤤ Linear pair :- when two adjacent angles are supplementary it means that they form a straight line (180°) then,they are called linear Pair.

⤤ Vertically opposite angle :- when two lines intersect at a point they form equal angle that are vertically opposite to each other.

Answer 2

Step-by-step explanation:

1233484848585858585848