Question

if two lines intersect, then the vertical angles are congruent. How do you prove that?

Answer 1

Proof: Let line AB intersect line CD at point O.

Angle AOC + Angle COB = 180, because AB is a straight line and therefore equal to 180.

By the same reasoning, Angle COB + Angle BOD = 180.

Since both sums are equal to 180, then Angle AOC + Angle COB = Angle COB + Angle BOD.

Now subtract Angle COB from both sides: Angle AOC = Angle BOD.