Question

Prove that if two lines intersect each other the vertically opposite angle formed are equal

Answer 1

Let AB and CD be two lines intersecting at 'O'.Two pairs of vertically opposite angles. 1. <AOD, <BOC 2. <AOC, <BOD
TO PROVE
1.<AOC=<BOD
2. <AOD=<BOC
PROOF
A ray OA stands on line CD
<AOC+<AOD=180°(Linear pair axiom ).......(1)
A ray OC stands on a line AB
<AOC+<BOC=180°(Linear pair axiom )..... (2)
from (1)and (2)
<AOC+<AOD=<AOC+<BOC
<AOD=<BOC
Similarly
<AOC=<BOD
HENCE PROVED!!!