Question

if two straight lines intersect at a point, prove that the vertically opposite angles are equal.(use linear pair axiom)​

Answer 1

Answer:

According to the problem, we need to prove that if two lines intersect each other, then the vertically opposite angles are equal. Let us draw the two lines AB and CD intersecting at point O. ... Now, let us consider the angles on the line AB. So, we get ∠COB+∠AOC=180∘ ---(2).

Answer 2

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

i.e. <AOC, <DOB, <AOB, <COB.

To prove :- <AOC = <DOB & <AOD= <COB

Proof :

<AOC + <AOD = 180° [linear pair] ___(1)

<AOD + <BOD = 180° [linear pair] ___(2)

from eq. (1) & (2)

<AOC + <AOD = <AOD + <BOD

i.e. [<AOC = <BOD]

Similarly [<AOD=<COB] Hence proved.