Question

given: ( x parallel y )
( w ) is a transversal of ( x ) and ( y ).
prove: ( angle 4 cong angle 5 )
complete the two - column proof.
a
b
c

Explanation:

Step1: Vertical angles theorem

Vertical angles are congruent. So, \(\angle4\cong\angle1\) (Reason A).

Step2: Corresponding angles postulate

When two parallel lines \(x\parallel y\) are cut by a transversal \(w\), corresponding angles are congruent. So, \(\angle1\cong\angle5\) (Reason B).

Step3: Transitive property of congruence

If \(\angle4\cong\angle1\) and \(\angle1\cong\angle5\), then \(\angle4\cong\angle5\) (Reason C).

Answer:

A. Vertical angles theorem
B. Corresponding angles postulate
C. Transitive property of congruence