Question

state and proof vertically opposite angle theoram​

Answer 1

Vertically opposite angle theoram
if two lines intersect each other than the pair of vertically opposite angles are equal .
Proof
given :ab and cd intersect at o
to prove:angle aod=angle cob
angle aoc =angle bod
proof:angle aod +angle aoc=180° (1) (linear pairs)
angle aod +angle bod=180 °(2) (linear pairs)
from (1) and(2)
we get ,
angle aod+angle aoc =angle aod +angle bod
angle aoc = angle bod
similarly,
angle aod =angle cob
hence proved
hope it helps