Question

What is the missing step in the given proof? Help me out with my math homework please!

Answer 1

D. I got you bro. its D

Answer 2

Answer: The missing step is,

m∠OCP ≅ m∠ABC because corresponding angles made by the same transversal on the parallel lines are congruent.

Step-by-step explanation:

Given : $AC \parallel BD$, $AB \parallel CD$

And, $AC \perp CD$

We have to Prove : Angle PCQ is complementary to  angle ABC

⇒ $m\angle PCQ + m\angle ABC = 90^{\circ}$

Proof:  Since, $AC \perp CD$

⇒  $m\angle OCQ = 90^{\circ}$

But,  $m\angle OCQ = m\angle OCP +m\angle PCQ$ ( By angle addition postulate )

⇒  $m\angle OCP +m\angle PCQ = 90^{\circ}$ ( By transitive property of equality )

Since, $AC \parallel BD$,

⇒ $\angle OCP\cong \angle ABC$ ( corresponding angles made by the same transversal are congruent)

⇒  $m\angle OCP = m\angle ABC$ ( By the definition of congruent angles )

This leads,

$m\angle ABC +m\angle PCQ = 90^{\circ}$  ( by the transitive property of equality )

Thus, by the definition of complementary angles,

Angle PCQ is complementary to  angle ABC

Hence proved.