Question 676702
Theorem 3.5 	If two parallel lines are intersected by a transversal, then corresponding angles are congruent.


Given: line AB is parallel to line CD

Prove: Corresponding angles are congruent

Proof:



 you have already learned vertical angles are congruent and corresponding angles are 
congruent if they are formed by parallel lines

using this information we can go on to prove alternate interior angles are also congruent if they are formed by parallel lines


since the lines are parallel, than

< 1 and < 3 are congruent, 
< 2 and < 3 are vertical angles

you have studied a theorem that states all vertical angles are congruent, so
that means < 1 congruent to < 3 because they are corresponding angles,

 and < 2 congruent to < 3  because they are vertical angles, 

that means < 1 must be congruent to < 3