geometry help please !! medal! What is the missing step in the given proof?
PCQ and ACP are supplementary by the Linear Pair Theorem.
For parallel lines cut by a transversal, corresponding angles are congruent, so ACB PCQ.
OCP BCD by the Vertical Angles Theorem.
For parallel lines cut by a transversal, corresponding angles are congruent, so OCP ABC.
For parallel lines cut by a transversal, corresponding angles are congruent, so OCA CBD.
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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.
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.
segment AC parallel to BD and AB is parallel to CD and AC id perpendicular to CD