Question

Prove that if two lines intersect each
other, then the vertically opposite angles
are equel​

Answer 1

Given,

Two lines, suppose AB and CD intersect each other.

As we know,

If two lines i.e., AB and CD intersect each other,they have two pairs of opposite angles -Angle AOC, Angle DOB, Angle AOD, Angle COB.

To proof : Angle AOC=Angle DOB

and Angle AOD=Angle COB

Proof:

Angle AOC +Angle AOD =180° (Linear pair) ...(i)

Angle AOD+Angle BOD =180° (Linear pair)... (ii)

From equation (i) and (ii),

Angle AOC +Angle AOD = Angle AOD+Angle BOD

Therefore, Angle AOC=Angle BOD

Similarly, Angle AOD and COB

Hence, proved.