How to solve the two column proof, If two lines form congruent adjacent angles, then they are perpendicular

Question

How do I solve the following proof.  If two lines form congruent adjacent angles, then they are perpendicular 

Answer 1

MRosen,

 

To form two angles, one line must cross the other.

 

Let the two angles formed on one side of the line be Θ and Φ , both measured in degrees or radians

 

Then  Θ + Φ = 180^o (or ∏ radians), since the sum of all the angles formed from one point (here the intersection point) on the same side of the line must be 180^o.

 

But Θ = Φ  by congruence, so substitute for theta in previous expression and get 2Φ = 180^o (or ∏)

Hence,  Φ = 90^o (or ∏/2) = Θ.