moriahgarcia
contestada

Given: AC||BD , AB||CD, and AC _|_ CD
Prove: ∠PCQ is complementary to ∠ABC.

Proof: Since AC _|_ CD m∠OCQ = 90° by the definition of perpendicular lines. By angle addition, we can say m∠OCQ = m∠OCP + m∠PCQ. But since m∠OCQ = 90°, m∠OCP + m∠PCQ = 90° by the Transitive Property of Equality. [Missing Step] By the definition of congruent angles, m∠OCP = m∠ABC. This leads to m∠ABC + m∠PCQ = 90° by the Transitive Property of Equality. So, based on the definition of complementary angles, ∠PCQ is complementary to ∠ABC. What is the missing step in the given proof?

A. ∠PQC and ∠ACP are supplementary by the Linear Pair Theorem.

B. For parallel lines cut by a transversal, corresponding angles are congruent, so ∠ACB ≅ ∠PCQ.

C. ∠OCP ≅ ∠BCD by the Vertical Angles Theorem.

D. For parallel lines cut by a transversal, corresponding angles are congruent, so ∠OCP ≅ ∠ABC.

E. For parallel lines cut by a transversal, corresponding angles are congruent, so ∠OCA ≅ ∠CBD.

Given ACBD ABCD and AC CD Prove PCQ is complementary to ABC Proof Since AC CD mOCQ 90 by the definition of perpendicular lines By angle addition we can say mOCQ class=

Respuesta :

lizvalle

Answer:

D. For parallel lines cut by a transversal, corresponding angles are congruent, so ∠OCP ≅ ∠ABC.

Step-by-step explanation:

Since we need to show the connection of the proof from m∠OCP + m∠PCQ = 90° by the transitive property of equality to the definition of congruent angles, m∠OCP= m∠ABC,  letter D which states that For parallel lines cut by a transversal, corresponding angles are congruent, so ∠OCP ≅ ∠ABC is the only statements that fits to what we need to show.

hippsaiden40

Answer:

answer is D

Step-by-step explanation:

m∠OCP + m∠PCQ = 90° by the transitive property of equality to the definition of congruent angles, m∠OCP= m∠ABC,  letter D which states that For parallel lines cut by a transversal, corresponding angles are congruent, so ∠OCP ≅ ∠ABC is the only statements that fits to what we need to show.

Otras preguntas