Given: || , and || .

Prove: PCQ is complementary to ABC.

Proof: Since , mOCQ = 90° by the definition of perpendicular lines. By angle addition, we can say mOCQ = mOCP + mPCQ. But since mOCQ = 90°, mOCP + mPCQ = 90° by the Transitive Property of Equality.

[Missing Step]

By the definition of congruent angles, mOCP = mABC. This leads to
mABC + mPCQ = 90° by the Transitive Property of Equality. So, based on the definition of complementary angles, PCQ is complementary to ABC.

Question

Given:   ||  , and  ||  . 
     

 Prove: PCQ is complementary to ABC.




Proof: Since    , mOCQ = 90° by the definition of perpendicular lines. By angle addition, we can say mOCQ = mOCP + mPCQ. But since mOCQ = 90°, mOCP + mPCQ = 90° by the Transitive Property of Equality. 

[Missing Step]

 By the definition of congruent angles, mOCP = mABC. This leads to 
mABC + mPCQ = 90° by the Transitive Property of Equality. So, based on the definition of complementary angles, PCQ is complementary to ABC.